Were both users set up under the same web-id through the panel? If that's the case, then just ssh in with the 'recieving' user and copy the files over. Something like "cp -r /home/userName/Domain.com/ Domain.com/"
The first directory path is the user who has the files you want to copy, the seconed path is where you want the files placed. "cp" copies so your origionals will still be in place.