The Book of Jasher is Deuteronomy
Anyone who is familiar with the Judaism directory at AskWhy! will know that it argues that Judaism began when the Persians sent colonists to Judah (Persian, Yehud) with a law that they were obliged to follow. Ezra is described as delivering this law in the bible itself sometime in the fifth century BC (417 BC can be inferred). The law was what is now called Deuteronomy. The bible seems to deliberately imply that Deuteronomy was accidentally found in the temple by Josiah, who used it to justify the reformation he introduced, or so most biblicist scholars think, but they think the bible is supernaturally true.
In fact, the myth of the accidental discovery of a book is one created by the Persians to make their own imposition of the new law more palatable to the local inhabitants who were Canaanites. The colonists, told they were descendants of Judahites and were “returning” to their proper home, were actually a ruling elite from somewhere else in the Persian empire—the clues suggest Beth Eden—and were being punished by deportation from their homeland to settle among and pacify the local Canaanites by instilling into them Persian ways and creating a temple state for the collection of tribute. If they succeeded, they became the ruling class of Yehud, and respected priests of the regional temple set up for people conquered by the Persians who were cooperative with them. Only the colonists originally were Jews. They were a nation of priests.
Of course, the bible does not actually name the Josiah law or the law Ezra read out. Another law for the followers of Moses must have been superfluous, one would have thought. Quite so. The supposed discovery of a law book and its implementation by Josiah around 610 BC, and the reading of yet another law by Ezra around 417 BC show that the story of Moses and the Exodus is mythical, a myth devised at a later date, in third century BC Egypt!
But the law given by the Persians was not called Deuteronomy, which is Greek for Second Law, the first supposedly being that of Moses. The new Law could simply have been called The Law, as it still is by the Jews. The attribution to Moses of course came with the later myth. But did it also have a name of its own. Perhaps so. The bible refers in several places (Joshua 10:12-13, 2 Samuel 1:19-29, 1 Kings 8:12ff LXX) to the Book of Yasher (Anglicized to Jasher). “Yasher” means “upright” or “righteous”. Jewish scholars will doubtless know this, but I have just come across confirmation that this was a name for the Law by this passage from the Babylonian Talmud:
R Eliezer says (Babylonian Talmud, Tract Abuda Zara) the Book of Yashar is Deuteronomy because there it is is written… “And thou shalt do that which is right (Yashar) and good in the eyes of the Lord” (6:18).
The point is that the measure of righteousness or uprightness for a Jew is the Law, and that was originally Deuteronomy.
Of course, what is now Deuteronomy is hardly likely to be what the Book of Yasher was at first. Chunks of it will have been deliberately erased to suit the later priesthood, free of Persian influence, and then subject to the Macedonians and the Hasmonaeans, and parts of it will have been expanded and set out in the previous law books that were written in Ptolemaic times, notably Leviticus.