Mosiah took the brass plates with him when he traveled down from the Land of Nephi into Zarahemla. The king, who was named Zarahemla, was "exceedingly" glad to finally see these plates which had the record of the Jews. Since Zarahemla was king, he probably was a descendant of Mulek, with a royal lineage that had attendant royal privileges. He probably did not know much about the details of where he came from, but Zarahemla probably did have knowledge that he was of royal blood and perhaps had knowledge that he was from some faraway place. The people of Zarahemla had lost their language, but that does not mean that they had completely lost all knowledge of their ancestral history.
Book of Mormon Central, "Why Should Readers Pay Close Attention to the Mulekites? (Omni 1:19)," KnoWhy 434 (May 17, 2018).