What is the fate of a Christian that believe God is one, has no son and Jesus is not God and that Muhammad and Jesus are Prophets and still remains a Christian and does not take Islam as a religion? Will God accept him?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Whoever is in the condition mentioned in your question is still considered a Kaafir (disbeliever). Only admitting that Allah is one and Jesus and Muhammad are merely Prophets does not make one a Muslim unless he firmly believes in Islam and willingly accepts it as his religion. Allah Says (what means):

• {And whoever seeks a religion other than Islam, it will never be accepted of him, and in the Hereafter, he will be one of the losers.} [Quran 3:85]

• {Indeed, the religion in the sight of Allah is Islam.} [Quran 3:19]

• {… and have chosen for you Islam as your religion.} [Quran 5:3]

The Prophet said: “(I swear) By Him in whose Hand is the life of Muhammad, he who amongst the community of Jews or Christians hears about me, but does not affirm his belief in that which I have been sent, and dies in this state (of disbelief), he shall be one of the denizens of Hellfire.” [Muslim]

Believing in the Prophet Muhammad and what has been revealed to him does not mean only to acknowledge his prophecy. There were some Jews who confessed the prophecy of the Prophet Muhammad ; even some polytheists had confessed his prophecy, but they were not considered Muslims.

Believing in the prophecy of Muhammad means having strong, unshakable belief in his Prophethood and acting according to it. Everyone who has true faith in the message and mission of Jesus definitely has faith in the prophecy of Muhammad also, as Allah Says on the tongue of Jesus (what means): {…And giving glad tidings of a Messenger to come after me, whose name shall be Ahmad.} [Quran 61:6]

Whoever does not have true belief in Muhammad as it should be, in fact, he does not have belief in Jesus either, in spite of his claim that he does.

Allah knows best.