Dear Brother, This is in answer to yours of the 9th inst., containing the following questions: (1) What authority have we as Latter-day Saints, in either modern or ancient revelation, or in sermons of our brethren, for the statement that the negroes are those who were neutral in heaven at the time of the great conflict or war? (2) Is it a fact that a Negro cannot receive the priesthood, and if so, what is the reason? Answer to question 1: So far as we know, there is no revelation, ancient or modern, neither is there any authoritative statement by any of the authorities of the Church of Jesus Christ of Latter-day Saints in support of that which many of our elders have advanced as doctrine, in effect that the negroes are those who were neutral in heaven at the time of the great conflict or war, which resulted in the casting out of Lucifer and those who were led by him, said to number about one-third of the hosts of heaven. Answer to question 2: You are referred to the Pearl of Great Price, Book of Abraham, Chapter 1, verses 26 and 27, going to show that the seed of Ham was cursed as pertaining to the priesthood; and that by reason of this curse they have no right to it.
While there is no written revelation going to show why the negroes are ineligible to hold the priesthood, the Prophet Joseph Smith is said to have explained it in this way, that by killing his brother, Abel, Cain deprived him of posterity, and this without doubt was the intent of Satan in tempting Cain to take his brother's life. And the Prophet Joseph is said to have added that the seed of Cain, however worthy, will not be eligible to bear the priesthood until after Abel shall have had posterity, and that means until after Abel's posterity shall have obtained earthly tabernacles, otherwise the children of the slayer would have advantages over those of the slain.
[Source: First Presidency, Letter to Milton H. Knudson, as quoted in Minutes of the Apostles of The Church of Jesus Christ of Latter-day Saints, 1835-1951, Electronic Edition, 2015]