There's not much that can be told to be honest. Most tips were given in this thread already.
I'm hoping your friend got it back, but if not, keep in mind that they need to send the most polite/well mannered request they can. Avoid typos and 'hello/good morning, please, thanks for your attention' are a must!
All they can do is explain that in the house there's more than one person using IMVU, and that the extra account was banned without reason. Keep in mind that there's a chance for IMVU requesting money to get the account active again, and if they can't pay, they won't get it back.
Other than that they can just keep their hopes up.
Good luck!