This is to say that a relative fixed this problem yesterday and now all is well. However, in case anyone else has the same problem here is the solution.
When Mozbackup is used to backup T'bird and Firefox, it associates each backup with a Profile kept in the AppData folder on the computer. It restores to this Profile if T'bird and Firefox have not been changed in the meantime. If they are deleted tho', say by an upgrade to Win 10, and then re-installed and used at all before a Restore is attempted, they will have a new Profile identity and the back-up will not recognise it.
To get a Restore it's essential not to use either of the progs before attempting it, and then to Restore to 'Default' as the choice in the Restore box. The computer will immediately create a new Profile identity to which the back-up file will restore - no problem.