Microsoft Authenticator account lost

Hello! Changing phones (my previous one died), I was able to back-up my Microsoft Authenticator app. All my profiles are there (email, work mail, etc), but the profile connected to my Facebook account is missing. Unfortunately Facebook told me that they cannot help me skip any step in order to get the recovery codes to re-connect Facebook to the Authenticator app.

Is there any way you can help me recover the access? Please, I do really need to access Facebook on my laptop (I got logged out)