In Deuteronomy 18:15-22 Moses states that the LORD would raise up a Prophet like him.  Who was this prophet?

Here is passage in full.

Deu 18:15  “The LORD your God will raise up for you a Prophet like me from your midst, from your brethren. Him you shall hear,
Deu 18:16  according to all you desired of the LORD your God in Horeb in the day of the assembly, saying, ‘Let me not hear again the voice of the LORD my God, nor let me see this great fire anymore, lest I die.’
Deu 18:17  “And the LORD said to me: ‘What they have spoken is good.
Deu 18:18  I will raise up for them a Prophet like you from among their brethren, and will put My words in His mouth, and He shall speak to them all that I command Him.
Deu 18:19  And it shall be that whoever will not hear My words, which He speaks in My name, I will require it of him.

The apostle Peter answered this question.  In speaking of Jesus Christ, Peter identified Him as this prophet quoting from Deuteronomy.

Act 3:20  and that He may send Jesus Christ, who was preached to you before,
Act 3:21  whom heaven must receive until the times of restoration of all things, which God has spoken by the mouth of all His holy prophets since the world began.
Act 3:22  For Moses truly said to the fathers, ‘THE LORD YOUR GOD WILL RAISE UP FOR YOU A PROPHET LIKE ME FROM YOUR BRETHREN. HIM YOU SHALL HEAR IN ALL THINGS, WHATEVER HE SAYS TO YOU.
Act 3:23  AND IT SHALL BE THAT EVERY SOUL WHO WILL NOT HEAR THAT PROPHET SHALL BE UTTERLY DESTROYED FROM AMONG THE PEOPLE.’

The prophet of Deuteronomy 18 is Jesus Christ.