A long awaited feature for the Microsoft Authenticator is coming soon on iOS first.
With this new feature, the Microsoft Authenticator app will be able to backup (and so restore) your accounts added onto the app.
This will be less painful when you have to re install the app either on a new device or after your device has been reset.
The functionality is currently under preview – aka beta. If you want to join the preview, register here https://forms.office.com/Pages/ResponsePage.aspx?id=v4j5cvGGr0GRqy180BHbR68AojHg485IuWUUpl99NURUNzJHT0c1QVBWWEFPNVFFNkpVM0xQUkJLQS4u with your Apple ID.