ON THROUGH-THE-FIST FLOURISH
There are a couple of aspects to consider regarding this move: (1) Its basic mechanics; (2) Its application or how it is used.
The first time I ran across this move was in Edward Marlos The Cardician (1953) in a trick titled Quick Sands (pp. 112-113), which uses a four-card packet. The purpose was to turn over the packet as it is pushed through the hand to apparently change the color of the backs from blue to red.
During the packet trick craze in the 70s, the same mechanics were extensively used as a flourish preceding transformations or reversals. It can be used to change or retain the disposition of the card, packet, or deck. In other words, it can be used to turn it over or not turn over.
As Max Maven points out, the same mechanics of using the thumb to push an object through a hand where the fingers are curled or closed and the hand turns from palm up to palm down has been used in cigarette manipulation, primarily to reproduce a thumb-palmed cigarette. It has also been applied to knives, paddles, and business cards as mentioned in At the Table (1984), pp. 157. In the aforementioned book I also said that the move was often credited to Dai Vernon. (See In Lieu of the Thru-the-Fist Flourish.). I published a short citation in Good Turns (1977) that made the analogy to the color-changing knife turnover and mentioned the Cardician reference.
The credit to Vernon is something I continually heard voiced by others, but I never found such a credit in print. The closest citation is in Dai Vernons Ultimate Secrets of Card Magic where Larry Jennings applied the move to a trick titled The Changing of the Guard (pp. 75-81). Karl Fulves credited Vernon when he wrote up and published Sam Schwartzs Back Flip but its exact provenance is not clear. (Karl Fulves called it Vernons Twisting Move, which creates a bit of confusion since many magicians associate the twisting move with the flat, horizontal, circular end-to-end movement used in the classic Twisting the Aces. The first time I saw the Through-the-Fist maneuver applied to a packet was in Bob Walkers Fisting the Aces, a routine I explained in my first set of lecture notes in 1975.
Much later I ran across the same maneuver in Thayers Magical Bulletin (March-1918) by Konnor; however, whereas Konnor uses the left thumb and the palm-up-to-palm-down mechanics, he applies it differently. He used a deck and uses the mechanics to make a single card (selection) rise from the top of the turned hand. He does not push the entire deck through the hand. If you look at the three illustrations, however, you get the impression of the Through-the-Fist mechanics. Close, but no cigar.
So, for some the matter of provenance is still an open question.
The basic mechanics precedes anything done with cards. The inventor? Beats me. It may be easier to credit Dai Vernon than to recite the capsulized history just given.
How you apply the mechanics is more important and that history is another matter.