A brother of our ward shared what he saw happen last week with us in Fast and Testimony meeting. He sat near the double doors that were open and watch as a woman with a scarf around her head in Muslim like fashion come in. She looked at the picture of the Savior with his 12 apostles for about 2.5 minutes and then prostrated herself on the floor in the state of Muslim worship. She got up, looked at the picture again and did the same thing. She did this a total of 3 times. At the end, this brother came to her and invited her into listen to conference. There was a language barrier, but she came and sat and listened probably not understanding much, but had tears streaming down her face often. At the end, he again tried to communicate with her, to no avail. He brought over the missionaries, again a language barrier. The only thing he could think of to do was to give her a picture of the Savior with the 13 articles of faith on the opposite side of a card he always carries with him in his wallet.
While listening to this story, my mouth dropped open! I can only speculate about why she was there and what she felt and what she knows or does not know.
I've heard of Muslim's being converted to Mormonism and explaining it to their people as Joseph Smith is the new Muhammad. I've heard of Muslims having dreams in which they were told that Muhammad is not a true prophet. I know of the similarities of our religions, such as a food code, the need for a prophet to restore doctrine, etc. Someday they will all be brought to the knowledge of Jesus Christ and we will all be under one King: The King of Kings.
For more information read this: A Latter-day Saint Perspective on Muhammad.
From the Wikipedia: (red words, created by me, are similar beliefs of The Church of Jesus Christ of Latter-day Saints)
According to Islamic tradition, each prophet conveyed the same basic ideas of Islam (defined as submission to God, to his words and to his orders). They brought the belief in a single God and in the avoidance of idolatry and sin. Each came to preach Islam and told of the coming of the final law-bearing prophet and messenger of God: Muhammad. Each prophet directed a message to a different group and each prophet taught minor variations in sharia (or the practice of religion) to a different target audience. These variations constitute applications of Islam: mainstream Muslims do not consider them discrete versions of Islam.
Islamic tradition holds that God sent messengers to every nation. Muslims believe that God finally sent Muhammad to "seal" and to convey the divine message to the whole world (to sum up and to finalize the word of God), whereas he had previously sent the other messengers (rusul) to convey their messages to a specific group of people or to an individual nation.
Muslims regard Adam as the first prophet and Muhammad as the last prophet; (from the traditional interpretation of Muhammad's title Seal of the Prophets). Islam regards Jesus as a rasul (and sometimes as a nabi) because he received wahy (revelation) from God, through which God revealed the Injil (Gospel) to him. Muslims have great respect for Jesus (known by the Arabic form of his given name as Eesa or Isa) and for his mother Maryam. They do not, however, regard Jesus as the son of God.