Messages restored from Time Machine in Library but not accessible from within MAIL
I have recently restored from Time Machine some important Mailboxes/messages, and I can navigate, with some difficulty, through Users/Me/Library/Mail/... to find the messages, but I can find no way to get them back in a Mailbox shown on the sidebar of MAIL, that is, to get the On My Mac Mailbox working as it did before the loss and restoration. If I can fix this problem for that mailbox, then I can possibly retrieve a number of other messages that have suffered the same fate.
Hope somebody can talk me through this.
MacBook Pro (15-inch Late 2011), OS X Mavericks (10.9.5)