Joseph Smith's use of the Egyptian Alphabet and Grammar continued
beyond the month of July. In October 1835 he is reported to have used
the Egyptian Alphabet to interpret some of the Egyptian artifacts.
See History of the Church, Vol.2, Ch.21, p.286:
What appears to be the Joseph Smith Egyptian Alphabet and Grammar has been published by the Modern Microfilm Company (Utah Lighthouse Ministry) in 1966. A copy of the document can still be obtained from them for approximately seven dollars. After looking over the document it is no surprise that Mormon scholars been making incredible rationalizations for its existence. Without going into to much detail I will present some evidence that you the reader can verify for yourself.
First, the hypocephalus (facsimile no. 2) shown on one of the pages of the Joseph Smith Egyptian Alphabet and Grammar shows missing portions. These same missing portions have been filled in on the facsimile no. 2 which is now in the Book of Abraham. The "filled in" portions of facsimile no. 2 have been shown to be reproductions from both the Sensen Text of Joseph Smith Papyri XI and a figure from Joseph Smith Papyri IV. So the Egyptian Alphabet and Grammar reproduction of the hypocephalus verifies the fact that Joseph Smith fabricated and altered sections of the facsimile no. 2.
Secondly, the text the Sensen text that is "translated" in the Egyptian Alphabet and Grammar. The word "translated" is used loosely here because one Egyptian character is aligned with an entire sentence of the Book of Abraham text. Obviously there is not enough information in one character to translate the amount of material that is shown in the Joseph Smith Alphabet and Grammar, yet this is what was done. Interestingly enough the same Sensen text that was used to fill in the missing portions of facsimile no. 2 are aligned in the columns of the "translated" Egyptian Alphabet and Grammar. In my opinion, it is obvious that Joseph Smith had written the Book of Abraham using his research on Abraham and then later reconstructed the Egyptian Alphabet and Grammar. This reverse engineering theory is the only logical alternative in my opinion.
I encourage you to look at how the missing portions were filled in by Joseph Smith on facsimile no. 2. Also, take a look at how a couple characters were aligned to the text of the Egyptian Alphabet and Grammar.