When Christ appeared to the people of the Americas, He gave the same command, and instituted the sacrament among them, in remembrance of His Atonement. Many churches, my own included, still observe this ordinance weekly, in remembrance of Christ.
Reading and thinking about the sacrament prayers last week made me realize something. I had always assumed that the bread of the sacrament was a token of Christ's mortal body, which He laid down as a sacrifice for us. So where the sacrament prayer says "that they may eat [the bread] in remembrance of the body of thy Son," I always just tacked on "which died for them," to parallel the other prayer's structure, "that they may do it [drink the water/wine] in remembrance of the blood of thy Son, which was shed for them" (see Moroni 4-5).
But Christ's command to the Nephites threw a different light on the whole subject. After instructing them to observe the ordinance of the sacrament, Christ said, in perfect parallel of the sacramental prayer, but inserting the missing phrase, "And this shall ye do in remembrance of my body, which I have shown unto you. And it shall be a testimony unto the Father that ye do always remember me. And if ye do always remember me ye shall have my Spirit to be with you" (3 Nephi 18:7).
So the body symbolized by the bread of the sacrament is not Christ's mortal body, but the body He showed to the Nephites--that is, His resurrected body. So the parallel structure in the prayer is not "that they may eat in remembrance of the body of thy Son, which died for them," but rather, "that they may eat in remembrance of the body of thy Son, which was resurrected for them."
Thus the sacrament becomes a two-fold emblem of Christ's mission of deliverance from death. The water/wine represents His atoning blood, which was shed for us in Gethsemane as He performed the Atonement, and which cleanses us from sin, or spiritual death. And the bread represents His resurrected body, which left an empty tomb and enabled each of us to overcome mortality, or physical death. By taking the sacrament, we recognize that the Savior whose Atonement we commemorate by partaking of the emblems of His flesh and blood holds the keys to both death and hell, that He has "ascended up on high, as also he descended below all things, in that he comprehended all things, that he might be in all and through all things, the light of truth" (Doctrine & Covenants 88:6).