We will separately check out how to turn on Cloud Backup for Microsoft Authenticator App On Android & iPhone phones.
Turn On Cloud Backup for Microsoft Authenticator app for Android
Enable Cloud Backup for Microsoft Authenticator app for iPhone
If you use an iOS device, you will have your Microsoft account set to have the data backed up. This backup will be stored on your OneDrive storage connect to the Microsoft account you signed in with.
If you wish, you can try these features on the Microsoft Authenticator for Android. I hope you found this guide useful! Read: How to use and add Work/School accounts to Microsoft Authenticator app.