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Why to make fresh install ? You can easily upgrade from 2.0.13 to 2.2.
But, if you really want I think you can make it like this:
- export your 2.0.13 database
- make a fresh install of 2.2
- import 2.0.13 database
- run xoopsupdate.php
- reinstall system module
I think this should work but I am not sure ... Off course make a backup!