Moses prophesied that the day would come when Jehovah would raise up, from within the nation of Israel, a prophet who would be like him in many respects. This coming prophet would speak divine words, and those who refused to hear his words would give account for such rebellion (Deuteronomy 18:15-19).
One does not have to speculate on the fulfillment of this prediction. The coming prophet was none other than Jesus Christ, as Peter affirms when he quotes this Old Testament passage in his great sermon in Acts 3 (see vv. 22,23).
The fact is, there were many similarities between Moses and Christ. Both were: leaders, prophets, law-givers, mediators, etc. For an extended list of likenesses (and contrasts as well) between Moses and Christ, see Burton Coffman, Commentary on Hebrews, pp. 67-69.
Bracket Deuteronomy 18:15-19 and in your margin write: Fulfilled in Christ; see Acts 3:22,23. Both were law-givers, mediators, etc.