Backup or Transfer Your Authenticator Account:

To protect your access, Salesforce Authenticator allows you to back up your connected accounts. This ensures that you won't lose access to your Salesforce orgs if you get a new phone or reinstall the app.

To back up your accounts:
  1. Open the Salesforce Authenticator app on your mobile device.
  2. Tap the menu or gear icon to open Settings.
  3. Select "Back Up Accounts".
  4. Sign in with your Salesforce account.
  5. Follow the prompts to complete the backup.
To transfer accounts to a new device:
  1. Install Salesforce Authenticator on your new device.
  2. Open the app and select "Restore from Backup".
  3. Sign in with the same Salesforce account used for backup.
  4. Your connected accounts will be restored.
Read full instructions on Salesforce Help
Authenticator Device Reset Help:

Do you need to change phones or have lost your phone?
If you backed up your Authenticator, follow the transfer accounts instructions for your Authenticator App above.
If you did not back up your Authenticator, please Contact Support.