I have a client using a different host that he wants to transfer his acoount to us. Under his current host he uses RvSiteBuilder same version as we do.

Question. He wants to use the current site under a new domain name with us and cancel the old domain. Is it possible to move the files to our server and will the new domain name work with the old files created under the old domain under a different host?

Yep. Just transfer the old account to the new server. Then go to cPanel/RVSiteBuilder. It will display project recovering page and you can restore it on your new servers. Then you can publish it to any domain name you want. (Make sure the new domain name already resolve to your server. )

To transfer the account you may use one of the following method.
1. Use cPanel transfer facility in WHM.
2. Copy files /home/{OLD_USER} to /home/{NEW_USER} manaully.