This change first appeared in French, in the Jan. 1905 issue of I'Illusionniste, Vol. 4 No. 37, p. 5, with a byline of Van Lamèche. Professor Hoffmann, in Later Magic, identified Van Lamèche as a Belgian magician, but there is reason to suggest that Van Lamèche (a probable pun: vend la mèche = reveal the secret) was a pseudonym of Jean Caroly, editor of L'Illusionniste, and that Van Lamèche or Caroly were performing the same function Ellis Stanyon did in his English journal of the same period, Magic: explaining tricks he had seen rather than invented.
The Snap Change didn't appear in English until three years later. W. H. Dilger published the move as “Change Cards by Snap of Finger” in The Sphinx, Vol. 6 No. 12, Feb. 1908, p. 144. Eight years later, H. Syril Dusenbery managed to get it into the pages of The Sphinx again, this time under the title “The Flip Change” in Vol. 16 No. 12, Feb. 1916, p. 232. He reports learning it from Theodore Bamberg, which probably occurred during an October 1914 meeting of the Pacific Coast Society of Magicians, where Dusenbery reports Bamberg performing the change (see The Sphinx, Vol. 13 No. 9, Nov. 1914, p. 169). Curiously, five years later Dunsenbery contributed the same sleight to Felsman's Magical Review, Vol. 2 No. 6, Nov. 1921 - Feb. 1922, p. 6. There he does not mention Bamberg and leaves the reader to assume the sleight is his (Dusenbery's) invention. The previous year Bamberg had published the sleight himself, in Quality Magic, 1921, p. 16.
Another who claimed the Snap Change was Stanley Collins. In his Gems of Personal Prestidigitation, 1952, p. 15 (not published until its inclusion in Edwin Dawes's Stanley Collins: Conjurer, Collectors, and Iconoclast, 2003), Collins claims that he came up with the sleight in his early twenties—which would place it in the first decade of the 1900s—and he showed it around that time to Horace Goldin, Harry Houdini and Chung Ling Soo. Further corroboration of Stanley's claim appears in The Wizard, Vol. 2 No. 17, Aug. 1948, p. 176, in a letter by R. C. Wilson; also see Victor Farelli's response in the Nov. 1948 issue, Vol. 2 No. 19, p. 247.
Horace Goldin is most frequently credited with this sleight, due to the “The Goldin 'Visible' Change” appearing in Victor Farelli's Farelli's Card Magic, Part Two, 1933, p. 70. Farelli wrote in The Wizard (cited above) that Goldin taught him the sleight in 1931. However, Walter B. Gibson, in his Complete Illustrated Book of Card Magic, 1969, p. 315, related that Goldin had shown him a manipulative routine using the Snap Change in the early 1920s, ten years before he demonstrated the Snap Change to Farelli. Goldin told Gibson that the routine was Felix Fabian's, a professional card manipulator from Philadelphia. When Gibson first wrote up the Fabian sequence for the July 1924 issue of The Sphinx, Vol. 23 No. 5, p. 164, he said of this change: “The first part of the trick is fairly well known.” This does not sound as if it is a claim of invention for Fabian, although it could be argued that the sleight might have been Fabian's and had circulated among magicians to the point of becoming well known in 1924. But since it had been published at that time under the names of several others (see above), one would expect Gibson would wish set the record straight if the sleight were Fabian's. However, there is another possibility. Goldin, via Gibson, ascribed the manipulative sequence to Fabian. The Snap Change may have been Goldin's invention, which Fabian incorporated into his sequence. While these entries leave us in doubt about the inventor of the Snap Change, its use by Fabian predates all claims of invention by Van Lamèche, Collins et. al., since Fabian died on May 5, 1899. Of the preceding claimants, this leaves only Goldin as a possible contender.