Item #2 comes from the archive of the same auction house that listed item #1. Included in both item listings was a LOA from the same authenticator approving both as authentic signed Robert Fitzsimmons autographs. Is this item more consistent with the other one they authenticated (#1) or more consistent with the one they would not authenticate and which was sold by me (#3)? How can an authenticator give their approval on two different autographs of the same subject, whose signature remained very consistent over time, which in no way show any resemblance to each other?

An authentic Fitzsimmons autograph, the authenticator got this one right.

Lot: 19567 Auction: 709 1912 Robert Fitzsimmons Signed Book.
Listed at number eight on the Ring Magazine list of the one hundred greatest punchers of all time, Fitzsimmons finds himself sandwiched between Jack Dempsey and George Foreman, whose devastating power is the stuff of legend. In fact, nine years before making a gift of this first edition copy of his Physical Culture and Self Defense book to a friend, his first-round knockout of Con Coughlin, known as "The Irish Giant," proved fatal, as Coughlin would succumb to his injuries the following day. Fitzsimmons' tremendous relevance as one of the sport's all-time greats is essentially inversely proportional to the availability of his autograph, and we must stress that the appearance of two signed pieces in this auction is due solely to the fact that both derive from the same source. Predating the handwritten letter also in this auction is this important hardcover volume, inscribed upon the opening page, "Fitzsimmons Farm, Dec. 12 - 1912, To Mr. Arthur J. Bigelow, With Best Wishes, Bob Fitzsimmons, 'a man's a man for a' that.'" The literary quotation at the end is a line from celebrated Scottish poet Robert Burns' work "Is There For Honest Poverty," which was adopted as a form of Scottish national anthem, though its use by a British-born New Zealander in this instance is a bit of a mystery. Regardless, the inscription remains marvelously bold in black fountain pen ink, and the "Fitzsimmons Farm" reference at the start could quite reasonably be considered a second example of this tough and important autograph. The rightmost two-thirds of the page is toned, most likely from a dust jacket that has since been lost, but the effect causes little visual concern. The leather covered volume is otherwise in fine shape, tightly bound with only typical edge and spine wear. LOA from James Spence Authentication