Although many Latter-day Saints (including perhaps Joseph Smith) have assumed the phrase "by his own hand, upon papyrus" meant Abraham himself physically wrote the papyri that came into the Prophet's possession, the phrase itself is actually found in texts from ancient Egypt and Israel, and should be taken to mean no more than attributing authorship to an individual.
There is a difference between the date of a text and the date of a manuscript or publication. The date of a text is the date of its composition, whereas the date of a manuscript is the date of any given extant copy. For example, just because a Bible was printed in 2005 doesn't mean that the original author in the Book of Isaiah isn't Isaiah even though he lived 2500 years earlier. It would be a copy of copies.
Text can be said to have been written by someone even if the text only survives in later manuscript copies, as is nearly universally the case with texts from the ancient world. As such, even if the surviving papyri date several centuries after Abraham's lifetime, that doesn't preclude the possibility of Abraham having written, dictated, or commissioned the text that bears his name. It would only mean that what Joseph Smith received was a later copy of the text.
Latter-day Saint author Kevin L. Barney outlines a plausible scenario for the transmission of the Book of Abraham (assuming the biblical patriarch wrote the text):
It seems . . . likely to me that, if Abraham composed the original text from which the Book of Abraham derives, then 1. Abraham may have composed the text in a Semitic language. Whether this would have been an East Semitic language, presumably some form of Akkadian (the Semitic lingua franca of its day), or a West Semitic language, presumably some sort of early Canaanite dialect (analogous to Ugaritic), is difficult to say. It certainly would not have been composed in Hebrew, which did not really come into existence as such until about 1200 B.C. Abraham may have written his text in cuneiform in a medium suitable to that type of writing, such as clay tablets. 2. Between the time of Abraham's composition of the text and the early second century B.C. (or first century A.D.) papyrus copies that later would come into Joseph Smith's possession, there was a transmission of the text. This may have included versional translation into Egyptian and, possibly, other languages (such as Hebrew), scribal copying, and, possibly, redaction of the text. 3. The facsimiles may not have originated with Abraham; rather, they may have become associated with the Book of Abraham as part of the redaction and transmission of the text.
This must be taken into consideration when one encounters the phrase "by his own hand, upon papyrus," at the beginning of the Book of Abraham. The author of the CES Letter fails to do so. This is a significant omission on his part, since this omission makes it seem as if the phrase "by his own hand, upon papyrus" invalidates the historicity of the text. It does not. Egyptologist Kerry Muhlestein explains more fully why:
Both members of The Church of Jesus Christ of Latter-day Saints and those of other faiths have often assumed that the statement, “The writings of Abraham while he was in Egypt, called the Book of Abraham, written by his own hand, upon papyrus,” (Book of Abraham, Heading) means that Abraham himself copied the writings onto the papyrus acquired by the Prophet Joseph. Critics have attacked this assumption because we can date the papyri we have, including Facsimile 1, to a time period after Abraham. We know exactly who the owner of this papyrus roll was, what his priestly offices and duties were, that he served and lived in Thebes, and the names of several generations of his family. The man who owned (and likely created) Joseph Smith Papyri fragments 1, 10, and 11 (which constitute the beginning of the roll that contains Facsimile 1) was Hor (Horus in its Greek form)—an influential priest in Thebes around the time of the creation of the Rosetta Stone (approximately 200 BC). His father was a governor of Thebes and held the same priestly position as his son. Horus would have been highly educated, literate, and likely conversant in several languages; he also would have had access to the great libraries of the temples in Thebes. I have already discussed the evidence showing that priests in Thebes during this time period had access to stories about Abraham. Thus the owner of this papyrus was an educated priest who probably had access to information about biblical figures. Interestingly, one of his priestly roles was associated with Egyptian execration rituals, which sometimes involved human sacrifice—something akin to what Abraham describes in the Book of Abraham and is depicted on Facsimile 1.
Critics say that if this papyrus was written in the second century BC it could not possibly have been written by Abraham himself. In regard to this assumption, I ask, who said this particular papyrus was written by Abraham himself? The heading does not indicate that Abraham had written that particular copy but rather that he was the author of the original. What these critics have done is confuse the difference between a text and a manuscript. For example, many people have a copy of J. R. R. Tolkien’s Lord of the Rings; each has a manuscript copy of the text that Tolkien originally wrote. A text, regardless of how many copies of it exist in the world, is written by one author. However, each copy of that text is a manuscript.
The earliest known copies of the book of Isaiah date to hundreds of years after the prophet’s death. Yet this has not led to the conclusion that Isaiah was not the author of the book of Isaiah. Clearly the manuscripts we have are copies of the original text that he wrote during his lifetime. We all know that when an author of the ancient world wrote something, if those writings were to survive or be disseminated, the text had to be copied again and again and again, for generation upon generation. When the heading states that the text was written by Abraham’s own hand, it notes who the author is, not who copied down the particular manuscript that came into Joseph’s possession. If critics had carefully thought through this issue, they would never have raised it.
These issues also highlight the question of how the Book of Abraham came to be in Egypt in the first place. There are a dizzying number of possibilities. Abraham himself was in Egypt, as was his great-grandson Joseph and all of his Israelite descendants for hundreds of years thereafter. After the Exodus, Israelites continued to travel to and live in Egypt. After the Babylonian destruction of Jerusalem, large groups of Jews settled in Egypt and created longstanding and thriving communities, even to the point that they built a temple. It was during this time period that Joseph Smith Papyri 1, 10, and 11 were created. Copies of these papyri could have moved back and forth between Egypt and Israel during any of these eras.
The author of the CES Letter fails to address any of these salient points in his superficial examination.
Additional Book of Abraham Resources:
FAIR Conversations, Episode 7: Brian M. Hauglid p.1, Brian M. Hauglid, 0:50:15A
FAIR Conversations, Episode 8: Brian M. Hauglid p.2, Brian M. Hauglid, 0:55:52
Mormon FAIR-Cast 62: “A Most Remarkable Book”, Tyler Livingston, 0:09:59
Mormon FAIR-Cast 139: “The Book of Abraham and the Prophetic Power of Joseph Smith,” Martin Tanner, 0:19:54