You should find a method of Restoring files from the Backup you created by launching CCC and looking for something like "Restore"
Once you have found it, and have it running, you should be able to select what you want to restore in the same was as you select what you want to backup.
Find the missing mailboxes in the list, select it and Restore.
I have IMAC processor 2.16 GHz core 2 intel Duo, start up Mac HD connected to a Lacie G5 external HD and has been a gem, and all these years my v good friend has put all puzzles in the right places for me, and now he has poorly brain, would like to help me but can't, as I am a new person to problems I am seeking help out here.
I do backup so I hope it has worked, my probby is that I have deleted a mailbox and some of it's babies, yes they are gone, I am thinking then, that if I backup again, the mailbox that was, will be deleted as of course, it's not there.
So what I want to know is, how do I get the mailboxes from the ccc back onto the Mac HD,if at all please