Source of this chess problem? [FEN "8/8/8/6pp/6pk/R7/6KP/8 w - - 0 1"]

1. Rh3+ gxh3+ 2. Kf3 g4+ 3. Kf4 g3 4. hxg3# 1-0


What is the source of this simple chess problem (White to mate in four) which somebody showed me at a chess club 50 or 60 years ago?

I suspect it's from the very early days of chess because it's so simple (no variations), and because of the unfashionable checking key, and because it involves only moves which have never changed in the history of chess (no queens or bishops or double-step pawn moves).

I tried searching the Meson Chess Problem Database and Yet Another Chess Problem Database without success, not sure I did it right.
I happened to find the position in an old book: on page 87 of "The Basis of Combination in Chess" by J. du Mont.  The diagram is shown with the names "Rubinstein vs N.", without date and place. Probably a game in a simultaneous exhibition.  The book was first published in 1938 and Dover reprinted it in 1978.