Mohammed couldn't just disregard Jesus, however, for he was too important. So he cleverly managed to make only the followers of Jesus evil while elevating Jesus to the rank of a prophet.
Mohammed had to convince people that Jesus was not the Son the God. If Jesus was the promised Messiah, there would have been no need for another prophet and no need for Mohammed because the prophecy would have been fulfilled.
The problem with this argument is, Jesus IS either the Son of God or He is a liar. To claim He was a prophet but also a liar just doesn't make sense.
Jesus teaches love and forgiveness and died so that we can receive forgiveness and salvation...if we choose to. Mohammed teaches hatred and revenge and his followers are really victims of a cult with no free will at all.
The Muslims claim that the Christians distorted the New Testament and likewise that the Jews distorted the Torah.
So they feel free to discount any inconvenient citations.
Lewis (if only on the basis of his little book The Abolition of Man) shows that the gift of prophecy is not lost in the West (even if it's a bit less impressive than the gift shown by recent Orthodox monastic elders).
I'm beginning to wonder whether the last of his children's novels doesn't contain a prophecy of the nature of the Antichrist--the 'Anti-Aslan' is a fraud supported by a Narnian arch-secularist and the Calormenes (thinly disguised Muslims), pushed on the basis of a 'we all worship the same god' syncretism.