I backed up my iPhone prior to taking it to Apple for repair, and ended up with a new iPhone.

When I tried to restore the backup onto my new iPhone however, iTunes informed me I have no backups available. I located the backup file under MobileSync/Backup but I can't get iTunes to recognise it.

I really only care about 1 specific Note, since I manually backed up my photos. Does anyone know how to restore the full backup, or even just get my Notes back?

AppleCare couldn't help me either. They said the version of iOS on the old iPhone being older than the one on the new iPhone might cause some sort of backward compatibility issue, but they couldn't offer any solutions.