Even though this is a hypothetical question, the simple answer is that a Muslim would weigh the message and see whether it appealed to their senses, seeking guidance from Allah.
This is no different to a non-Muslim accepting Islam today, or a Muslim continuing to believe in Islam.
As far as I know, all prophets confirmed the prophets before them and introduced the ones to come after them. Muhammad (pbuh), being unique in that there wasn't going to be a prophet after him, confirmed the prophets before him like other prophets but unlike other prophets, he informed us that there would be no further prophets after him.
He prophesied the return of Jesus (as), but as a follower, rather than again as a prophet.
This is a question I do personally grapple with as well, because Muslims of a certain period of time will be faced with similar questions, i.e., how do we recognize Dajjal? How do we recognize Jesus (as)? How do we recognize the Mahdi?
While none of them are going to be prophets, I think in spirit, the problem is similar and the answer lies in http://quran.com/2/26.
Indeed, Allah is not timid to present an example - that of a mosquito
or what is smaller than it. And those who have believed know that it
is the truth from their Lord. But as for those who disbelieve, they
say, "What did Allah intend by this as an example?" He misleads many
thereby and guides many thereby. And He misleads not except the
Short version: keep a seeking, open mind.