That is true, mohammed is a false prophet.
To belive mohammed means disbeliving many of the prophets and the disciples of Jesus or those close to them, such as.
Isaiah(written 750BC)
Surely he took up our infirmities and carried our sorrows, yet we considered him stricken by God, smitten by him, and afflicted. But he was pierced for our transgressions, he was crushed for our iniquities; the punishment that brought us peace was upon him, and by his wounds we are healed. We all, like sheep, have gone astray, each of us has turned to his own way; and the LORD has laid on him the iniquity of us all. Isaiah 53:4-6
Beliving mohammed means disbeliving the central theme of the whole new testiment, Jesus paid for your sins so you dont have too in hell, if you repent and trust in him. This theme of the atonement is supported by the many different writers of the bible, in the old testament there was the sacrificing of the spotless animals to pay for sin(which was just a forrunner for the atoning sacrifice Jesus made), and in the new testament direct references are made to the atonment Jesus made for those willing to accept him.This righteousness from God comes through faith in Jesus Christ to all who believe. There is no difference, for all have sinned and fall short of the glory of God, and are justified freely by his grace through the redemption that came by Christ Jesus. God presented him as a sacrifice of atonement, through faith in his blood. He did this to demonstrate his justice, because in his forbearance he had left the sins committed beforehand unpunished- he did it to demonstrate his justice at the present time, so as to be just and the one who justifies those who have faith in Jesus. Romans 3:22-26
Hebrews 9 talks about this issue, by contrasting the old covenant to the new.
He did not enter by means of the blood of goats and calves; but he entered the Most Holy Place once for all by his own blood, having obtained eternal redemption. The blood of goats and bulls and the ashes of a heifer sprinkled on those who are ceremonially unclean sanctify them so that they are outwardly clean. How much more, then, will the blood of Christ, who through the eternal Spirit offered himself unblemished to God, cleanse our consciences from acts that lead to death, so that we may serve the living God! For this reason Christ is the mediator of a new covenant, that those who are called may receive the promised eternal inheritancenow that he has died as a ransom to set them free from the sins committed under the first covenant.
In the case of a will, it is necessary to prove the death of the one who made it, because a will is in force only when somebody has died; it never takes effect while the one who made it is living. This is why even the first covenant was not put into effect without blood. When Moses had proclaimed every commandment of the law to all the people, he took the blood of calves, together with water, scarlet wool and branches of hyssop, and sprinkled the scroll and all the people. He said, "This is the blood of the covenant, which God has commanded you to keep." In the same way, he sprinkled with the blood both the tabernacle and everything used in its ceremonies. In fact, the law requires that nearly everything be cleansed with blood, and without the shedding of blood there is no forgiveness.
It was necessary, then, for the copies of the heavenly things to be purified with these sacrifices, but the heavenly things themselves with better sacrifices than these. For Christ did not enter a man-made sanctuary that was only a copy of the true one; he entered heaven itself, now to appear for us in God's presence. Nor did he enter heaven to offer himself again and again, the way the high priest enters the Most Holy Place every year with blood that is not his own. Then Christ would have had to suffer many times since the creation of the world. But now he has appeared once for all at the end of the ages to do away with sin by the sacrifice of himself. Just as man is destined to die once, and after that to face judgment, so Christ was sacrificed once to take away the sins of many people; and he will appear a second time, not to bear sin, but to bring salvation to those who are waiting for him. Hebrews 9:12-28
From a objective view why would someone belive one mans message over the central message of the many who were there or close to those who were? As blueman said quite well.