I notice ISPConfig Panel does not show client when examining mailbox settings. I wanted to move some mailbox accounts from one client to another. The mail domain does have client, and seems to allow changing to another client. Does this move also the mailboxes with @thatdomain to the other client?
Yes. All mailboxes of a domain must be owned by the same client, you can't move just some of them to another client, at least not by using the ISPConfig GUI. It might be possible to manually change the sys_groupid in the database, but as soon as you would change something in the email domain, the ownership will probably be changed back.