Actually, the first FIVE BOOKS (called the “Pentateuch”) of the Bible are believed to have been written largely by Moses. The Lord Jesus referred to these 5 books as “the Law of Moses” in Luke 24:44, “Then He (Jesus) said to them, ‘These are the words which I spoke to you while I was still with you, that all things must be fulfilled which were written in THE LAW OF MOSES and the Prophets and the Psalms concerning Me.’” In Matthew 19:8 the Lord Jesus refers to Moses as the author of Deuteronomy 24:1-4: “He (Jesus) said to them, ‘Moses, because of the hardness of your hearts, permitted you to divorce your wives…” Here are some examples from the Pentateuch citing Moses as the author:

“Then the LORD said to MOSES, ‘WRITE THIS for a memorial in the book and recount it in the hearing of Joshua, that I will utterly blot out the remembrance of Amalek from under heaven” (Exodus 17:14).

“These are the journeys of the children of Israel, who went out of the land of Egypt by their armies under the hand of Moses and Aaron. Now MOSES WROTE DOWN the starting points of their journeys at the command of the LORD” (Numbers 33:1-2).

“So MOSES WROTE THIS LAW and delivered it to the priests, the sons of Levi…” (Deuteronomy 31:9).

We conclude from this that even though others (like Joshua) may have actually written the original manuscripts, the revelations in those manuscripts were given to Moses by God. This is confirmed in God’s words to Joshua in Joshua 1:7-8, “Only be strong and very courageous, that you may observe to do according to ALL THE LAW WHICH MOSES MY SERVANT COMMANDED YOU….THIS BOOK OF THE LAW shall not depart from your mouth, but you shall meditate in it day and night, that you may observe to do according to all that is written in it.”

I said at the beginning the Pentateuch was “believed to have been written LARGELY by Moses.” He could not have written all of it, for as you intimated some of it was written after his death. We read of his death in Deuteronomy 34:5-8, “So Moses the servant of the LORD died there in the land of Moab, according to the word of the LORD. And He buried him in a valley in the land of Moab, opposite Beth Peor; but no one knows his grave to this day. Moses was one hundred and twenty years old when he died.” It is quite possible that Joshua was the author of these words. This is the LAST CHAPTER of the LAST BOOK of the Pentateuch, so it is safe to assume that the vast majority of the Pentateuch was indeed written by Moses up until his death.

In closing, you do raise a valid question as to why Moses wrote in the THIRD PERSON instead of the FIRST PERSON, but there are historians who have done the same thing. Their purpose has been to give a historical account (and not an autobiography) and thus they chose to refer themselves in the third person. Moses was most likely doing the same thing. Or, as stated earlier, others may indeed have “written the original manuscripts” (though “the revelations in those manuscripts were given to Moses by God”) and they would then naturally refer to Moses as Moses. (329.5) (DO)