The crystals are microscopic and ride with the vapor - and since it doesn’t melt it adheres to the lungs; look it up.
Looked it up. Didn’t see anything that looked remotely scientific. I remain unconvinced. Body temperature average is 98.6 F. The burning coal of the cigarette vaporizes the menthol sprayed on the tobacco cut filler. With a melting point range of 97-100 F, I am highly skeptical that menthol vapor recrystallizes in the lungs. Old-timers will remember a home remedy for colds was to put a small amount of Vicks Vapor Rub just inside there nostrils. The active ingredient is menthol. Menthol is used in peppermint candies, though that is a different route of consumption.