Migration assistant didn't seem to migrate my OS X Mail mailboxes and content

I used Migration Assistant to copy a user account from a Time Capsule backup (of a Lion machine) to a Mavericks machine. The Lion machine Mail app used the Google IMAP connection.

The behavior of Mail.app surprised me. Initially it appeared empty, though mailbox folders were present. Then, overnight, messages appeared to transfer from Gmail. They didn’t appear to have been migrated from the original machine.

Curious. I couldn’t find much about this on the net, so for now I’ll share without comment.