Where did W. W. Phelps find out about “ancient shorthand Egyptian”?

What really happened in the meeting between Charles Anthon and Martin Harris? Robert F. Smith, Gordon C. Thomasson, and John W. Welch explain one vital clue:

According to Martin Harris, Joseph Smith copied some of the Book of Mormon characters and Martin took them to New York. There he met with Charles Anthon, who certified to him that they were correct. Completely reassured, Harris returned to Harmony, told his friends about it, and later mortgaged his property to finance the publication of the Book of Mormon. This is very early concrete evidence that Martin Harris’s version of his meeting with Anthon is accurate and that Anthon’s later retraction was an attempt to save face, if not an act of downright dishonesty.
Shortly afterwards, in 1831 W. W. Phelps wrote a letter in which he reported that Anthon had translated the Book of Mormon characters and declared them to be “the ancient shorthand Egyptian.” This is a most telling clue, for where else, except from Anthon, would Harris and hence Phelps have gotten this precise phrase, the phrase shorthand Egyptian? It was not part of Harris’s environment or education.1 Indeed, the phrase is so singular that it appears only this one time in LDS history.
On the other hand, this precise term was known to scholars, Anthon included. In 1824, Champollion had used an equivalent term, “tachygraphie,” in his landmark Préçis du système hieroglyphique des anciens Égyptiens (a copy of which Anthon owned), to describe hieratic Egyptian script. In June 1827, this book was reviewed in the American Quarterly Review, calling hieratic Egyptian script “short-hand” Egyptian. Anthon knew this review: He owned a copy and he cited it in his Classical Dictionary. Anthon would have read this review only months before Harris’s visit.
Thus it becomes highly probable that Phelps indeed heard this peculiar phrase from Harris, who in turn got it from Anthon, the only person involved who was likely to have known it. Anthon probably mentioned shorthand Egyptian because he was struck by certain obvious similarities in the transcript to hieratic or demotic Egyptian. From this, what else can one conclude, except that Harris told the truth about what Anthon said on this point?…
– Robert F. Smith, Gordon C. Thomasson, and John W. Welch, “What Did Charles Anthon Really Say?,” in Reexploring the Book of Mormon, edited by John W. Welch (Provo, Utah: FARMS, 1992), Chapter 19

What are the odds that Charles Anthon would say the characters were shorthand Egyptian when the Book of Mormon says it was written in reformed Egyptian?

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