Origins of the ``baby Freiman'' theorem

It is a basic folklore fact from the area of additive combinatorics that a subset $A$ of an abelian group satisfies $|2A|<frac32,|A|$ if and only if $A$ is contained in a coset of a (finite) subgroup $H$ with the density $|A|/|H|>frac23$. What are the historical origins of this fact? It was certainly known to Freiman around years 1961-1965, but I suspect that it can appear somewhere in the earlier papers by Kemperman / Scherk / Mann / Olson.