I would also like to know this! I have two Android devices using firefox sync. I've had to reinstall my desktop OS, and now want to set up firefox sync on the desktop machine again. Unfortunately I've lost my recovery key. Is there no way to retrieve it? I don't want to lose all my synced data!
oh sorry, i didn't consider that & look close enough :-/
forum member cor-el has created a modified version of the addon which might work reportedly, see https://support.mozilla.org/en-US/questions/942893
I could not find a way to do what we wanted to, however, the problem was solved for me in a different manner.
It syncs using the info from you phone. The tricky part was the sync option is not in firefox, it is in the operating systems settings.