Do Latter-day Saints believe Muhammad is a prophet?

I know this is an old question, but I thought I'd provide some additional perspective.

First, though, we need to define what a prophet actually is (from an LDS perspective). In Preach My Gospel, the LDS Church's official training manual for its missionary program, a prophet is defined as:

A man who has been called by and speaks for God. As a messenger of God, a prophet receives priesthood authority, commandments, prophecies, and revelations from God. His responsibility is to make known God’s will and true character to mankind and to show the meaning of His dealings with them. A prophet denounces sin and foretells its consequences. He is a preacher of righteousness. On occasion, a prophet may be inspired to foretell the future for the benefit of mankind. His primary responsibility, however, is to bear witness of Christ.

From this definition, we learn (among other things) two attributes of a prophet that are particularly relevant to this question:

1. A prophet's primary responsibility is to testify of the divinity of Christ as the Son of God, and the Savior of all mankind.
2. A prophet must receive priesthood authority from God to build up his (God's) church.

Since Latter-day Saints don't believe Muhammad received priesthood authority (see D&C 42:11), and he didn't testify of Christ, he would not qualify as a prophet.

However, that does not mean Mormons reject the possibility that some of Muhammad's teachings could be inspired of God. From the Book of Mormon:

For behold, the Spirit of Christ is given to every man, that he may know good from evil (Moroni 7:16)

More specifically, the following quote directly references Muhammad (see link to Preach My Gospel above for details):

Just as the Christian world was blessed by the courage and vision of the reformers, many other nations and cultures have been blessed by those who were given that portion “that [God] seeth fit that they should have” (Alma 29:8). Teachings of other religious leaders have helped many people become more civil and ethical.

While the teachings of Muhammad and others are not considered authoritative like the teachings of the prophet, Mormons believe that there is much truth and goodness that comes from the teachings of others not of their faith. Brigham Young (the second LDS prophet) stated:

It is our duty and calling, as ministers of the same salvation and Gospel, to gather every item of truth and reject every error. Whether a truth be found with professed infidels, or with the Universalists, or the Church of Rome, or the Methodists, the Church of England, the Presbyterians, the Baptists, the Quakers, the Shakers, or any other of the various and numerous different sects and parties, all of whom have more or less truth, it is the business of the Elders of this Church...to gather up all the truths in the world pertaining to life and salvation, to the Gospel we preach,...to the sciences, and to philosophy, wherever it may be found in every nation, kindred, tongue, and people and bring it to Zion (Teachings of Brigham Young).

In short, the answer to the question is no, Mormons don't consider Muhammad to be a prophet. They do, however, believe that much of what he taught is good, and of God.

While Latter-day Saints respect the beliefs of others, they don't revere or recognize Muhammad as a prophet.

In LDS history, the first prophet in our dispensation (a consecutive period of time where the gospel is on the earth and revealed, or "dispensed," through prophets) was Joseph Smith. Before that, the last prophet we have record of is Moroni, son of Mormon, who compiled The Book of Mormon. That was about 421 A.D, well before Muhammad's time.