As someone who has tweaked their UI more times than I can count, here's what you do. I might ***** this up a bit since I'm on my netbook right now and can't go into the WTF folders myself to check that i have the paths right, but I'll double check when I get home in an hour and a half.
You need to log in to your account in WoW first on his computer, then exit the game. Under the WTF folder, in the Account folder, you will see your pre-battle.net account name. Double click your account's folder, then delete everything inside the folder, and copy/paste your WTF files into your account folder.
Then make sure that you have all the necessary add ons installed in your add on folder.
I don't know how you're planning on doing this, but either from a USB stick or doing it manually over the network is probably the best bets.