This effect has two histories, the first in the seventeenth century, the second in the twentieth.
The seventeenth-century history was discovered only in 2017, by Reinhard Müller, who ran across a report of four unusual playing cards that had been preserved as evidence in the record of an arrest made in 1623 in Augsburg, Germany. The cards were initially believed to have been made for card cheating, but their nature was, to anyone knowledgeable in the methods of card cheating, useless for that purpose. The cards, though, in part fitted a familiar pattern for the method of an old transformation of the faces of four cards, which Sa. Rid first explained in 1612 in The Art of Jugling, or Legerdemaine. The trick probably dates to the 1500s, as descriptions of its performance by Girolamo Scotto during that period were recorded. But the cards confiscated in 1623 were peculiar because they included a double-backed card and a divided-face card, half of the face of which was a back. After much thought, Reinhard Müller realized that these cards seem suitable for only one purpose: The card trick explained by Rid, but with one phase in which the faces turned into backs. Thus, the All-Backs effect, in a brief form, was performed to an unknown extent in the 1600s. Full details of these cards and Müller's theory are given by Minch and Müller in “The Augsburg All-Backs”, Gibecière, Vol. 14 No. 2, Summer 2009, p. 123.
The second history of the All-Backs effect began in the early 1900s. Jean Hugard's “All Backs” was advertised in The Sphinx, Vol. 28 No. 11, Jan. 1930, p. 462, and used an ungimmicked pack. Karl Fulves reprinted the Hugard instructions, adding illustrations, in Verbatim, No. 9, 1993, p. 107-112. However, David Ben has evidence that Dai Vernon showed Hugard his version of this original plot around 1920. See Dai Vernon: A Biography, 2006, p. 167–8.
Edward Marlo, in The Cardician, 1953, p. 196, claimed the plot was established by R. W. Hull with the marketing of his NRA Deck in the 1920s. However, the earliest ad for Hull's NRA Deck seems to be in Sphinx, Vol. 32 No. 9, Nov. 1933, p. 287, where Hull advertised it as “Hull's New 'NRA' Deck.” Thus, Hull's rough-and-smooth deck came in third to Vernon's and Hugard's sleight-of-hand methods. Hugard published Vernon's method in an added chapter to the third edition of Expert Card Technique, 1950, p. 459.
None of these methods involved a chosen card. Hugard worked privately on that task, but never published his method. He did describe it in a letter to Orville Meyer, dated July 18, 1939. See Gibecière, Vol. 7 No. 1, Winter 2012, p. 159.