Hi Natalie,
Thank you for posting question to Microsoft Q&A.
According to this issue, may I know if your boss could access to his account's Security Info via this link: https://mysignins.microsoft.com/security-info ?
He should be able to remove the Microsoft Authenticator which has been prompting on your phone and then click on "Add Sign-in Method" > select Microsoft Authenticator > register MFA on Microsoft Authenticator on his phone. (He still needs to get to the link I provided above which should prompt Microsoft Authenticator on your phone first).
Please let me know if you have any further questions.
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