Jailbreaking does not prevent you from doing anything which your iPad could do before it was jailbroken. iTunes operates exactly the same way, oblivious to the fact you have jailbroken. You can still purchase and sync apps from the app store, sync your music, movies, and pictures. No difference.
If your neighbours refuses to sync he has likely done something else other than just jailbreaking. The most common cause of not being able to sync with iTunes is where a user has decided to install pirated applications. We have a strong anti-piracy stance on these forums (see rules in my sig) so we do not assist users with those kinds of problems to resolve them. If however it is for another reason, your neighbour is free to join here and ask for help
Hope that clarifies.