But afaik the Duchess of Fife wore the famous Fife tiara at the coronation in 1937, while her sister Maud, the Countess of Southesk, wore the amethyst tiara of Queen Alexandra. It was at the 1953 coronation that Maud wore the emerald tiara we are speculating about.
So maybe Princess Louise left it directly to Maud in 1939?