From what I gather the Book of Yasher is of Rabbinic origin, the oldest reference we have to it dates to 1565 C.E. And the oldest manuscript to about a century later. So I wouldn't put much stock.

It's much like the Book of Enoch. To believe it existed is to believe that it was before the time of slavery in Egypt, that it was kept the entire time they were in Egypt, carried with them trough the desert, and not once was it ever mentioned, either in Towrah or historical documents. The one exception with the "Book of Yasher" is in Yahowsah 10:13 which reads is it not written in the Book of Yasher? But when you understand that Yasher in Hebrew mean the upright or the upright one, so it could just as easily read the book of The Upright One and since Upright One is a title for God I would argue that this is not talking about some unknown book that dated to the time of Noah, but rather just the book of God, the Towrah.

But even if there were once a Book of Yasher, what we have today dates at the earliest to 1500s, way to long after it was scribed to be considered trustworthy.

and the story is that it is a copy from an ancient copy that survived the destruction of Jerusalem under Titus, made its way to Sevilia, and from there to Napuli, Spain. 12 identical copies were found...probably from Egypt under Ptolemy from the eral of the Septuagint. Also there were Greek copies from that era. I'm going to try get the story straighter from Ken Johnson, if I can.