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Within the Backup module there is a folder called 'cache' you have to chmod this folder to 777 in order for the module to save the backed up files into it.
In most FTP programs if you right click the folder then select properties or chmod or change permissions or something like that you can chmod the folder that way, it will also have something like User, Group, World then Read, Write and Execute underneath that, Read, Write and Execute has to be checked for User, Group and World or sometimes you can just type in 777.
Hope this helps.