How would Joseph Smith guess an association between a pharaoh contemporary to Abraham and a “crocodile” god?

The Book of Abraham’s facsimile 1, figure 9 depicts a crocodile and is described by Joseph Smith as “The idolatrous god of Pharaoh.”

Pearl of Great Price Central writes:

From evidence unknown in Joseph Smith’s day, we can say the following about “the god of Pharaoh” in the Book of Abraham and Facsimile 1. First, the god in question is most likely the crocodile deity Sobek. Second, among other things, Sobek was closely associated with the Pharaoh of Egypt. Third, Sobek was especially venerated by king Amenemhet III, a pharaoh contemporary to Abraham. Fourth, and finally, specimens of Sobek iconography have been recovered from the likely region of Abraham’s homeland during the right period for Abraham’s lifetime (the Middle Bronze Age).
– Pearl of Great Price Central – Sobek, The God of Pharaoh

What are the odds that Joseph would have gotten this right?

See:

Pearl of Great Price Central – Sobek, The God of Pharaoh

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