Upon a cursory reading of this verse one may wonder why Jesus is quoting this part of Malachi’s prophecy in light of the fact that the law of Moses was fulfilled in Christ.
The answer could possibly be that the Lord (and Malachi) were not referring to the Mosaic code and carnal commandments but rather to a different law that was given to Moses in Horeb—a higher law, even the fulness of the gospel that, because of Israel’s rebelliousness and stiffneckedness, they never were able to fully receive (see JST, Exodus 34:1-2; D&C 84:23-25; Teachings, p. 323).
If this is in fact the case, this reference is particularly relevant to both the Nephites and the latter-day Church. This seems to be the correct interpretation in light of the verses that follow and the essential role of Elijah in their having the fulness of gospel blessings.