The problem is that the user you’ve created is a new user and the rights assigned to this user are the rights assigned for the ‘Everyone’ group in the former profile. To resolve this issue, you have to simply copy (not move….) the documents to a new location
if all you did was rename the profile directory then it is not a new user. that user will still have the same SID that applies to those files. the problem is that you, and not the user, created the new profile directory. after you rename the old directory let them login to create the new one. that will set all proper permissions on the folder. then log them out and copy the files over. That should have given them the correct permissions. If not then have them log out, then right click the folder, go to properties. under security give that user full rights to the folder. then go under advanced and put a checkmark in REPLACE PERMISSIONS ON ALL CHILD OBJECTS WITH ENTRIES SHOWN HERE THAT APPLY TO CHILD OBJECTS. This will set those permissions on all files and subfolders within the directory.