waldviertler
I have used Affa to move servers, but essentially it is still doing a backup and restore, although somewhat differently. Affa should transfer all MYSQL data, users and config etc, just as a backup and restore SHOULD do. You will still have to reinstall contribs.
If the built in backup and restore is not working for you, then perhaps you have discovered a bug and should report your experience to bugzilla so the underlying issue can be resolved, for the benefit of yourself and other users.
I suspect something is not right with your original system eg file corruption, installed contribs conflicting, administrative configuration errors, changed root and/or MYSQL password ????
On your original system you could try running
signal-event post-upgrade
signal-event reboot
to ensure it is "clean" and then run the backup again.
What is the history of the original server, what contribs installed, what modifications made, is it working correctly etc ???
Ok, I've tried this procedere 3 times - does not work
What does "does not work" mean. Please provide more details of the errors or problem or part of the procedure where you have an issue appear, quoting real error messages etc.
No one here can possibly guess what "does not work" means.