Microsoft 365 features that help users manage their subscriptions, account settings, and billing information.
You can refer to AI’s answer first, as it covers the steps for moving Microsoft Authenticator authentication from your old phone to your new phone.
One additional point is that, because this is a university work or school account, the authentication methods available to you are controlled by your university. If you are unable to complete the registration on the new phone, especially if you lose access to the old phone, please contact your university IT/help desk. They can assist with resetting your authentication methods so that Microsoft Authenticator can be registered again.
After you regain access, it is also a good idea to add another sign-in method if your university allows it. Microsoft recommends having multiple sign-in methods associated with a work or school account to help avoid being locked out if one method becomes unavailable.
Sign in to your work or school account using two-step verification | Microsoft Support
You can manage the authentication methods for your account here: https://mysignins.microsoft.com/security-info
I hope this information helpful and if you have any further questions, please feel free to ask!