Even though the sacramental prayers are not recorded until Moroni 4–5, the Savior’s statement (“ye do always remember me.… [Y]e shall have my Spirit to be with you”) is sufficiently close to the prayer on the bread (Moro. 4:3) to provide assurance that it was the origin of the sacramental prayers. (See commentary accompanying Moroni 4–5.)
During this time, Nephi3-as-author is making this record after the fact. He did not record the prayers here (as he also omitted Jesus’s prayer over the children), but they must have been preserved in the large plates. Moroni would have been able to write them down from that source, if not from the personal knowledge of all believers.