Who proved that a triangulation is 3-colourable implies its dual is bipartite
This result is included in Ore's book The Four-Colour Problem (see Theorem 7.4.3).
I saw a paper that states this as a folklore result and cites Ore. Interestingly, the book gives a different proof for (ii)$\implies$(i). It seems that at that time, it wasn't known that the mapping $f\longmapsto f^*$ is a bijection.
Sorry to disappoint; but that's the best I could trace back.