Your on link says it was invented in winter 1942/43, WWII didn't end until September 45. That's plenty of time to train, equip, and utilize the technology in warfare. This article may not have been about Aquq-lung, but your book may have been accurate.
"The Aqua-Lung was invented in France during the winter of 1942–1943 by two Frenchmen: the engineer Émile Gagnan and the Naval Lieutenant Jacques Cousteau."