Bitfinex.com doesn't seem to give a backup/recovery key in case your Google2Factor Authenticator phone is lost or breaks down. The Authenticator app on Android doesn't have any sort of backup functionality.
On your Google's account you seem to be able to enable 2 factor authentication but that is for google authentication it seems. I.e I can't see how to backup the keys on the phone.
When you first set up GA for Bitfinex you were shown a secret key for GA to write down that would allow you to restore GA to a new phone if needed. They probably should really insist that you write that secret key down. Without that key you are in for a spot of bother if you lose the phone.
Didn't show the restore key at first. I am going to send them a ticket.