Robert Millet notes that Jacob's language concerning the fall of Adam is unmistakably similar to that of the language of God to Adam, as found in Joseph Smith's translation of Genesis:
Therefore I give unto you a commandment," the Lord said to our first father, "to teach these things [the plan of salvation] freely unto your children, saying: That by reason of transgression cometh the fall, which fall bringeth death . . . even so ye must be born again into the kingdom of heaven. (Moses 6:58-59; JST, Gen. 6:61-62)
Note the similarity to Jacob's teachings, based, it would appear, upon the brass plates: "There must needs be a power of resurrection, and the resurrection must needs come unto man by reason of the fall; and the fall came by reason of transgression" (2 Nephi 9:6).
For a more detailed study of the possible ties between the JST and the brass plates, see Robert L. Millet, "The Brass Plates: An Inspired and Expanded Version of the Old Testament," in The Old Testament and the Latter-day Saints, Proceedings of the 1986 Sidney B. Sperry Symposium (Salt Lake City: Randall Book Company, 1986), pp. 415-43). [Robert L. Millet, "Redemption Through the Holy Messiah," in Studies in Scripture: Book of Mormon, Part 1, pp. 128-129]