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See Hugard's Magic Monthly, Vol. 2, No. 12, May 1945, p. 119, “The Secret Addition” by Fred Braue, for the first appearance of this sleight. In this article, the basic sequence is described, but with the packet held face down, making it necessary to flip each card face up on the deck, then face down again. In Hugard's Magic Monthly, Vol. 3, No. 2, July 1945, p. 135, “The Secret Addition” Braue reports of an improvement he has recently made to the handling, which is to hold the packet face up, making the process more economical, as each card need only be flipped over once. This is the handling commonly used today. In Hugard's Magic Monthly, Vol. 3, No. 3, August 1945, p. 145, “The Secret Addition Again”, Corporal D. M. Amann from India, suggests that the extra cards be secretly dropped onto the third card as it is flipped face down on the deck. This leaves the fourth card a single one, which can be handled in the same way as the previous three, rather than dropping the packet onto the deck, then flipping over the last card.
In Marlo's Magazine, Volume Four, 1980, pp. 231-232, Marlo reports having developed all the above by 1944, and implies that information may have been leaked to Braue through various channels, although he then comments that it is too late in the game to argue about the credit.