Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
Dear Antoine DBS,
Welcome to Microsoft Community.
We understand that you cannot obtain the authenticator information and log in normally after migrating your mobile phone account.
According to your description, you tried to back up the account information on your old phone but still saw an error when you opened it on your new phone. You can try to refer to the following link to help you confirm the use and operation information of the authenticator:
Troubleshoot problems with Microsoft Authenticator - Microsoft Support
Back up account credentials in Microsoft Authenticator - Microsoft Support
Meanwhile, issues related to Authenticator require more professional technical information to help you solve them. I suggest you try to seek help in Microsoft learn (English only), where there are more experts in related fields who can provide you with better solutions.
It is designed to support advanced users like you. Many users prefer to ask questions and get more professional responses through this section.
Here is a link to the forum where you can raise specific situations and share your ideas for solving problems.
Microsoft Authenticator - Microsoft Q&A
We will keep this issue on file in case our great volunteers come up with ideas for you.
Best regards
Zenobia.Z | Microsoft Community Support Specialist