How do we know Moses wrote the entire Pentateuch?

[Jon]

Moses died but it seemed Deuteronomy can still be written? Was there another writer apart from Moses who recorded the 2nd group of Israelites that entered Canaan? Need some answers on these. Thanks!

[searchinmyroots]

Jon,

Good question, keep them coming!

So of course we don't really know the 100% accurate answer, but if I'm not mistaken, there are 2 schools of thought on this.

One being the entire Torah was given to Moses during his 40 days with G-d on the mountain. So he knew beforehand of his  death before reaching the promised land.

The second is that Joshua wrote the end of Deuteronomy after Moses died.

Others here might also chime in if they have anything to add or say.

[Robert]

Talmud, Baba Bathra 15a:

The Master has said: "Joshua wrote the book which bears his name and the last eight verses of the Pentateuch. This statement is in agreement with the authority who says that eight verses in the Torah were written by Joshua, as it has been taught: So Moses the servant of the Lord died there. Now is it possible that Moses being dead could have written the words, 'Moses died there'? The truth is, however, that up to this point Moses wrote, from this point Joshua wrote. This is the opinion of Rabbi Judah, or, according to others, of Rabbi Nehemiah." [But] Rabbi Shimon said to him: "Can the scroll of the law be short of one word? ... No; what we must say is that up to this point the Holy One, blessed be He, dictated and Moses repeated and wrote, and from this point God dictated and Moses wrote with tears."

English translation source: 
https://aish.com/48931547/

I have copied the above from the stated Aish webpage, on which there is commentary (analysis) of this extract from the Talmud.
As can be seen, there is a dispute whether Moses wrote the end of Deuteronomy as dictated by G-d, or if Joshua wrote it; just as moderator "searchinmyroots" has pointed out.