I think I solved this issue. 
This below, is /xdonations/includes/common.php according with the code in include/common.php contained in 2.2.3 version:
 /************************************************************************/ 
/* Donations - Paypal financial management module for XOOPS 2           */ 
/* Copyright (c) 2004 by Xoops2 Donations Module Dev Team                */ 
/* http://dev.xoops.org/modules/xfmod/project/?group_id=1060            */ 
/* $Id: common.php,v 1.5 2004/10/15 17:58:57 blackdeath_csmc Exp $      */ 
/************************************************************************/ 
/*                                                                      */ 
/* Based on NukeTreasury for PHP-Nuke - by Dave Lawrence AKA Thrash     */ 
/* NukeTreasury - Financial management for PHP-Nuke                     */ 
/* Copyright (c) 2004 by Dave Lawrence AKA Thrash                       */ 
/*                       thrash@fragnastika.com                         */ 
/*                       thrashn8r@hotmail.com                          */ 
/*                                                                      */ 
/************************************************************************/ 
/*                                                                      */ 
/* This program is free software; you can redistribute it and/or modify */ 
/* it under the terms of the GNU General Public License as published by */ 
/* the Free Software Foundation; either version 2 of the License.       */ 
/*                                                                      */ 
/* This program is distributed in the hope that it will be useful, but  */ 
/* WITHOUT ANY WARRANTY; without even the implied warranty of           */ 
/* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU     */ 
/* General Public License for more details.                             */ 
/*                                                                      */ 
/* You should have received a copy of the GNU General Public License    */ 
/* along with this program; if not, write to the Free Software          */ 
/* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307  */ 
/* USA                                                                  */ 
/************************************************************************/ 
 
// This is a stripped-down version of XOOPS common.php, with web-specific code removed.     
 
    // ############## Activate error handler ############## 
    include_once XOOPS_ROOT_PATH . '/class/errorhandler.php'; 
    $xoopsErrorHandler =& XoopsErrorHandler::getInstance(); 
    // Turn on error handler by default (until config value obtained from DB) 
    $xoopsErrorHandler->activate(true); 
     
    set_magic_quotes_runtime(0);     
    include_once XOOPS_ROOT_PATH.'/class/logger.php';     
    $xoopsLogger =& XoopsLogger::instance();     
    $xoopsLogger->startTime();     
    define('XOOPS_DB_CHKREF', 0); 
     
    // ############## Include common functions file ##############     
    include_once XOOPS_ROOT_PATH.'/include/functions.php';     
 
    // #################### Connect to DB ##################     
    require_once XOOPS_ROOT_PATH.'/class/database/databasefactory.php';     
    $xoopsDB =& XoopsDatabaseFactory::getDatabaseConnection();     
 
    // ################# Include required files ##############     
    require_once XOOPS_ROOT_PATH.'/kernel/object.php';     
    require_once XOOPS_ROOT_PATH.'/class/criteria.php';     
 
    // #################### Include text sanitizer ##################     
    include_once XOOPS_ROOT_PATH.'/class/module.textsanitizer.php';     
 
    // ################# Load Config Settings ##############     
    $config_handler =& xoops_gethandler('config');     
    $xoopsConfig =& $config_handler->getConfigsByCat(XOOPS_CONF);     
 
    // #################### Error reporting settings ################## 
    error_reporting(0); 
 
    if ($xoopsConfig['debug_mode'] == 1) { 
        error_reporting(E_ALL); 
    } else { 
        // Turn off error handler 
        $xoopsErrorHandler->activate(false); 
    } 
 
    // ################# Include version info file ##############     
    include_once XOOPS_ROOT_PATH."/include/version.php";     
 
    // #################### Include site-wide lang file ##################     
    if (file_exists(XOOPS_ROOT_PATH."/language/".$xoopsConfig['language']."/global.php")) {         
        include_once XOOPS_ROOT_PATH."/language/".$xoopsConfig['language']."/global.php";     
    } else {         
        include_once XOOPS_ROOT_PATH."/language/english/global.php";     
    }     
 
    // ################ Include page-specific lang file ################     
    if (isset($xoopsOption['pagetype']) && false ===strpos($xoopsOption['pagetype'], '.')) {         
        if (file_exists(XOOPS_ROOT_PATH."/language/".$xoopsConfig['language']."/".$xoopsOption['pagetype'].".php")) {                                    include_once XOOPS_ROOT_PATH."/language/".$xoopsConfig['language']."/".$xoopsOption['pagetype'].".php";         
        } else {             
            include_once XOOPS_ROOT_PATH."/language/english/".$xoopsOption['pagetype'].".php";         
        }     
    }     
    $xoopsOption = array();     
    if ( !defined("XOOPS_USE_MULTIBYTES") ) {         
        define("XOOPS_USE_MULTIBYTES",0);     
    } 
 
?>  
I replaced that above with the one below, according with the code in include/common.php contained in 2.0.xx version:
 /************************************************************************/ 
/* Donations - Paypal financial management module for XOOPS 2           */ 
/* Copyright (c) 2004 by Xoops2 Donations Module Dev Team                */ 
/* http://dev.xoops.org/modules/xfmod/project/?group_id=1060            */ 
/* $Id: common.php,v 1.5 2004/10/15 17:58:57 blackdeath_csmc Exp $      */ 
/************************************************************************/ 
/*                                                                      */ 
/* Based on NukeTreasury for PHP-Nuke - by Dave Lawrence AKA Thrash     */ 
/* NukeTreasury - Financial management for PHP-Nuke                     */ 
/* Copyright (c) 2004 by Dave Lawrence AKA Thrash                       */ 
/*                       thrash@fragnastika.com                         */ 
/*                       thrashn8r@hotmail.com                          */ 
/*                                                                      */ 
/************************************************************************/ 
/*                                                                      */ 
/* This program is free software; you can redistribute it and/or modify */ 
/* it under the terms of the GNU General Public License as published by */ 
/* the Free Software Foundation; either version 2 of the License.       */ 
/*                                                                      */ 
/* This program is distributed in the hope that it will be useful, but  */ 
/* WITHOUT ANY WARRANTY; without even the implied warranty of           */ 
/* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU     */ 
/* General Public License for more details.                             */ 
/*                                                                      */ 
/* You should have received a copy of the GNU General Public License    */ 
/* along with this program; if not, write to the Free Software          */ 
/* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307  */ 
/* USA                                                                  */ 
/************************************************************************/ 
 
// This is a stripped-down version of XOOPS common.php, with web-specific code removed.     
 
    // ############## Activate error handler ############## 
              global $xoopsLogger, $xoopsErrorHandler; 
     
              include_once XOOPS_ROOT_PATH . '/class/logger.php'; 
              $xoopsLogger =& XoopsLogger::instance(); 
    $xoopsErrorHandler =& $xoopsLogger; 
              $xoopsLogger->startTime(); 
              $xoopsLogger->startTime( 'XOOPS Boot' ); 
     
    set_magic_quotes_runtime(0);     
    include_once XOOPS_ROOT_PATH.'/class/logger.php';     
    $xoopsLogger =& XoopsLogger::instance();     
    $xoopsLogger->startTime();     
    define('XOOPS_DB_CHKREF', 0); 
     
    // ############## Include common functions file ##############     
    include_once XOOPS_ROOT_PATH.'/include/functions.php';     
 
    // #################### Connect to DB ##################     
    require_once XOOPS_ROOT_PATH.'/class/database/databasefactory.php';     
    $xoopsDB =& XoopsDatabaseFactory::getDatabaseConnection();     
 
    // ################# Include required files ##############     
    require_once XOOPS_ROOT_PATH.'/kernel/object.php';     
    require_once XOOPS_ROOT_PATH.'/class/criteria.php';     
 
    // #################### Include text sanitizer ##################     
    include_once XOOPS_ROOT_PATH.'/class/module.textsanitizer.php';     
 
    // ################# Load Config Settings ##############     
    $config_handler =& xoops_gethandler('config');     
    $xoopsConfig =& $config_handler->getConfigsByCat(XOOPS_CONF);     
 
    // #################### Error reporting settings ################## 
              if ( $xoopsConfig['debug_mode'] == 1 || $xoopsConfig['debug_mode'] == 2 ) { 
                  error_reporting(E_ALL); 
                  $xoopsLogger->enableRendering(); 
                  $xoopsLogger->usePopup = ( $xoopsConfig['debug_mode'] == 2 ); 
              } else { 
                  error_reporting(0); 
                  $xoopsLogger->activated = false; 
              } 
 
    // ################# Include version info file ##############     
    include_once XOOPS_ROOT_PATH."/include/version.php";     
 
    // #################### Include site-wide lang file ##################     
    if (file_exists(XOOPS_ROOT_PATH."/language/".$xoopsConfig['language']."/global.php")) {         
        include_once XOOPS_ROOT_PATH."/language/".$xoopsConfig['language']."/global.php";     
    } else {         
        include_once XOOPS_ROOT_PATH."/language/english/global.php";     
    }     
 
    // ################ Include page-specific lang file ################     
    if (isset($xoopsOption['pagetype']) && false ===strpos($xoopsOption['pagetype'], '.')) {         
        if (file_exists(XOOPS_ROOT_PATH."/language/".$xoopsConfig['language']."/".$xoopsOption['pagetype'].".php")) {                                    include_once XOOPS_ROOT_PATH."/language/".$xoopsConfig['language']."/".$xoopsOption['pagetype'].".php";         
        } else {             
            include_once XOOPS_ROOT_PATH."/language/english/".$xoopsOption['pagetype'].".php";         
        }     
    }     
    $xoopsOption = array();     
    if ( !defined("XOOPS_USE_MULTIBYTES") ) {         
        define("XOOPS_USE_MULTIBYTES",0);     
    } 
 
?>  
Now the IPN test of Xdonations 1.9beta works properly with XOOPS 2.0.xx.
I'm sorry for my dreadful English. I hope you understand what I mean.
Greetings,
Luca