You are not being very clear about "User Accounts" and what exactly your problems are. You just say it doesn't work, so what I say below I am guessing a bit
There are two separate ways of refering to the account - by the name the user logs in as - so if he logs in as "user" his data is typically stored in /home/user and subdirectories under it.
Secondly - each user has a "uid" (user id) which is a number normally for users starting at 1000 and increasing. The mapping from user to uid is in the /etc/passwd file. Controlling file access is via uid.
If you copy data between machines and the uids of the users don't match, then you will have access problems.