The cessation of the Law was to coincide with the consummation of the mission and atonement of Jesus Christ.
As important as was his sinless life, his peerless teachings, and his immaculate example, the Law—which was but a type of his great and last sacrifice (see Alma 34:13-14)—could only be completely fulfilled in the sacrifice and death of the Lamb of God (see 3 Nephi 1:24-25).
The Law of Moses was as one grand prophecy of the Savior and his atonement; Christ fulfilled the Law in the sense that he was the realization, the fulfillment of the prophecy.
After his death and ascension, while visiting the Nephites the Master taught:
“The law which was given unto Moses hath an end in me. Behold, I am the law, and the light. Look unto me, and endure to the end, and ye shall live.”
(3 Nephi 15:8-9; italics added )