There is divergent opinion among Christian and Muslim scholars about the ‘Prophet’ mentioned at Deuteronomy; 18:18-19 and John 1:20. Both claims are being analysed here:
God speaks to Prophet Moses: “I will raise them up a Prophet from among their brethren, like unto thee, and I will put my words in his mouth; and he shall speak unto them all that I shall command him. And it shall come to pass, that whosoever will not harken unto my words which he shall speak in my name, I will require it of him”(Deuteronomy; 18:18,19).
Among the prophets which followed Moses, Muhammad is most like Moses where as Jesus had nothing common with Prophet Moses except being a Jew and prophet, (though in Christianity, Jesus is believed to be Son of God, one of the three persons of the Trinity). Moreover, being descendent of Ishmael, Muhammad is among the brethren of Jews, who was like Moses.
Similarities: Moses & Muhammad :
Muhammad and Moses had a normal birth through father and a mother, while Jesus was miraculously born without any male intervention. (Mathew; 1:18 and Luke; 1:35 and also Qur’an;3:42-47).
Both were married, had children and died natural deaths. Muhammad (peace be upon him) is from among the brethren of Moses being descendent of Abraham through his sons Ishmael and Isaac respectively.
Prophet Muhammad (peace be upon him) was unlettered, hence in verbatim repeated the revelations conforming phrase; “Words in the mouth”. Prophet Moses & Muhammad (peace be upon them) brought new laws and new regulations for their people, besides, both were accepted as messengers of God by their people in their lifetime. They ruled over their communities (as kings), they could inflict capital punishment where as Jesus (peace be upon them) said, “My kingdom is not of this world.” (John; 18:36), Jesus was not accepted by most of his people in his life time: “He came unto his own, but his own received him not.”(Gospel of John;1:11) and he (Jesus) did not bring any new laws, Jesus said; “Think not that I have come to abolish the law and the prophets; I have come not to abolish them but to fulfill them..;”(Mathew;5:17-18).
Song of Solomon: Prophet Muhammad is mentioned by name in the Old Testament:
“His mouth is most sweet: yea, he is altogether lovely (Muhammadim). This is my beloved, and this is my friend, O daughters of Jerusalem.”(Song of Solomon; 5:16). :”Hikko Mamittakim we kullo Muhammadim Zehdoodeh wa Zehraee Bayna Jerusalem.“” In the Hebrew language ‘im’ is added for respect. Similarly ‘im’ is added after the name of Prophet Muhammad to make it Muhammadim. In English translation they have even translated the name of Prophet Muhammad (peace be upon him) as “altogether lovely”, but in the Old Testament in Hebrew, the name of Prophet Muhammad (peace be upon him) is still present.