The authorship of Deuteronomy may traditionally be attributed to Moses, but it is self evident that Moses wasn’t responsible for its climax:
“And Moses the servant of the Lord died there in Moab, as the Lord had said. He buried him in Moab, in the valley opposite Beth Peor, but to this day no one knows where his grave is. Moses was a hundred and twenty years old when he died, yet his eyes were not weak nor his strength gone. The Israelites grieved for Moses in the plains of Moab thirty days, until the time of weeping and mourning was over. Now Joshua son of Nun was filled with the spirit of wisdom because Moses had laid his hands on him. So the Israelites listened to him and did what the Lord had commanded Moses. Since then, no prophet has risen in Israel like Moses, whom the Lord knew face to face, who did all those signs and wonders the Lord sent him to do in Egypt—to Pharaoh and to all his officials and to his whole land. For no one has ever shown the mighty power or performed the awesome deeds that Moses did in the sight of all Israel.” (Deuteronomy 34:5-12)
Not only was Moses dead, the phrases “but to this day” and “since then” suggest Moses had been long dead. Just one reason why I think its important to read the books as books, from beginning to end, and meditate upon the Bible before accepting a tradition as biblical.