Move site from one customer to another?

We've got a client currently entered under his own customer record. Our webmaster tells me that the site actually belongs with a different customer record. Can I move this site from his current customer record to a different customer record, perhaps by manually manipulating the isp_dep table?

 

There's a tool to move web sites from one client to the next one under Tools.

 

Hot diggity! I had never seen that before.