Install Microsoft Authenticator on your new phone
Open Microsoft Authenticator on your old phone
Back up your accounts on the old phone if backup is enabled
On the new phone, sign in with the same Microsoft account used for backup
Open Microsoft Authenticator on the new phone
Tap Begin recovery or Restore from backup
Follow the prompts to restore your accounts
Verify each account on the new phone if required
Keep the old phone until all accounts are working on the new phone
Remove the accounts from the old phone after confirming the transfer
Re-register any accounts that do not restore automatically