I have watched this video a number of times over the years (it is not a new production). For those that are interested in one Latter-day Saint’s view of the video, please see:
A Response to the Video “The Lost Book of Abraham: Investigating a Remarkable Mormon Claim”, by Michael D. Rhodes, Associate Research Professor, Department of Ancient Scripture, Brigham Young University.
Rhodes also presented on the same topic at an LDS apologetics conference in 2003. The videos of the presentation can be seen
here.
There is also a response published by Ben McGuire through FAIR (Foundation for Apologetic Information and Research), which can be read here:
Responding To Errors in An Anti-Mormon Film: “The Lost Book of Abraham: Investigating a Remarkable Mormon Claim”.
A few other articles that I find particularly helpful in understanding Latter-day Saint perspective on this issue, and provide fascinating insights into not only the translation of the Book of Abraham, but also insights into the actual
text of the scripture, including fascinating parallels with other ancient writings on Abraham that Joseph Smith was of course not aware of in the 1800s include:
- “The Jewish Origin of the Book of Abraham” by Jonathan Moyer
- “New Light On the Joseph Smith Papyri” by John Gee (Research Professor at Brigham Young University, PhD in Egyptology, Yale University)
- A Critical Analysis of The Book of Abraham In Light of Extra-Canonical Jewish Writings by Rabbi Nissim Wernick (PhD Dissertation, Department of Graduate Studies in Religious Instruction, Brigham Young University)
LDS apologist Jeff Lindsay has a series of articles on the Book of Abraham that provide brief summaries of the issues commonly brought up by critics, as well as issues not commonly brought up by critics:
- Questions About the Book of Abraham Part 1: Sources of the BoA
- Part 2: Evidences For Plausibility
- Part 3 (my favorite): Ancient Records Offer New Support For the Book of Abraham
From these articles and videos, we see that the issue of the translation of the Book of Abraham is not as clear cut as the video in the OP would have us believe (and as we see from the reviews of the video, there are quite a number of problems with the arguments it makes and the evidences it presents), and for a book that many critics would have us believe Joseph Smith and/or his associates simply made up in the 1800s, there are many fascinating parallels with other ancient Judeo-Christian extra-canonical works on Abraham, including aspects of Abraham and his life that are not found within the Old Testament record.
I hope this helps for those interested in Latter-day Saint perspectives on the Book of Abraham.