A group of Microsoft Products and technologies used for sharing and managing content, knowledge, and applications.
Dear Nicola,
Good day, thanks for querying in this forum, we’re happy to help you.
From your description, it seems that you cannot sign in your Facebook account, you have set Microsoft Authenticator for it, however, you still cannot sign in successfully.
If my understanding is right, we’d love to help you, since our category focus on general troubleshooting and built-in features in Office 365 products, the question you mentioned is related to sign in issue of Facebook account and Microsoft Authenticator, we’d suggest you go to Microsoft Authenticator - Microsoft Q&A to post a new thread, which is specific channel to handle such situation. The engineers in related team will focus on your specific scenario and provide specific suggestions.
If the scenario above is not consistent with yours, you can also post back and point that.
Your understanding and patience will be highly appreciated. I hope that you are keeping safe and well!
Sincerely,
Sukie | Microsoft Community Moderator