To evangelize Muslims you have to convince them how could a demon come to Prophet Mohammed asking him to teach people that God is One. Arabs back then were worshipping statues and demons were very happy seeing them do so.
It is not that difficult to believe that Prophet Mohammed was visited by an angel, Angel Gabriel, because the teachings of Islam can no way be brought to us by demons.
Consider that demons might be the onse who visited those who came up with the idea that Jesus is the son of god, and that he said to people worship me as god, and that god allowed his son to die to clean your sins, and that he was raised in the third day. This shows that you are actually not worshipping one God, as father was alive and son was dead for three days, so one is alive and one is dead, how come they are one?
For Muslims, Jesus is so honored and loved, but to say that he is god, sorry, God is only One, He has no son, He is not like us who need to eat and sleep, He is the creator of heavens and earth, and He sent Prophet Jesus to ask people to worship God alone.
And for those who are wondering why would God send another Prophet after Jesus and another revelation, it is obviously because there was a strong need for that, people started believing in things that Jesus did not teach, there was a need for Islam, the submission to God, to guide people to the One True God, as people started contributing partners with Him, the Almighty.
Quran 5. They do blaspheme who say: “Allah is Christ the son of Mary.” But said Christ: “O children of Israel! worship Allah, my Lord, and your Lord.” Whoever joins other gods with Allah―Allah will forbid him the Garden and the Fire will be his abode. There will for the wrong-doers be no one to help. (72) They disbelieve who say: Allah is one of three in a Trinity: for there is no god except One God. If they desist not from their word (of blasphemy), verily a grievous penalty will befall the blasphemers among them. (73) Why turn they not to Allah and seek His forgiveness? For Allah is Oft-Forgiving, Most Merciful. (74) Christ the son of Mary was no more than an Messenger; many were the Messengers that passed away before him. His mother was a woman of truth. They had both to eat their (daily) food. See how Allah doth makes His Signs clear to them; yet see in what ways they are deluded away from the truth! (75) Say: Will ye worship, besides Allah, something which hath no power either to harm or benefit you? But Allah,― He it is that heareth and knoweth all things." (76) Say: "O people of the Book! Exceed not in your religion the bounds (of what is proper), trespassing beyond the truth, nor follow the vain desires of people who went wrong in times gone by― who misled many, and strayed (themselves) from the even Way. (77) Curses were pronounced on those among the Children of Israel who rejected Faith by the tongue of David and of Jesus the son of Mary: because they disobeyed and persisted in Excesses. (78) Nor did they (usually) forbid one another the iniquities which they committed: evil indeed were the deeds which they did. (79) Thou seest many of them turning in friendship to the Unbelievers. Evil indeed are (the works) which their souls have sent forward before them, (with the result) that Allah’s wrath is on them and in torment will they abide. (80) If only they had believed in Allah, in the Prophet and in what hath been revealed to him, never would they have taken them for friends and protectors but most of them are rebellious wrong-doers. (81) Strongest among men in enmity to the Believers wilt thou find the Jews and Pagans; and nearest among them in love to the Believers wilt thou find those who say: “We are Christians:” because amongst these are men devoted to learning and men who have renounced the world, and they are not arrogant. (82) And when they listen to the revelation received by the Messenger, thou wilt see their eyes overflowing with tears, for they recognise the truth: they pray: "Our Lord! we believe; write us down among the witnesses. (83) “What cause can we have not to believe in Allah and the truth which has come to us, seeing that we long for our Lord to admit us to the company of the righteous?” (84) And for this their prayer hath Allah rewarded them with Gardens with rivers, flowing underneath their eternal Home. Such is the recompense of those who do good. (85) But those who reject Faith and belie our Signs,― they shall be companions of Hell-Fire. (86).
