Hi John,
This forum is now in archive so for future posts use this one.
To answer your question...
Yes, he will be able to play his music quite happily
When he sets up his network at his new house the router will give his B2 a new IP address just as it will give a new address to his computer/tablet/phone.
When he uses the web UI or app he just needs to point it at the new IP address of his B2.
John