ANSWER: This cool fish is a slingjaw wrasse (Epibulus insidiator) or telescope fish. As the name suggests, unlike most other wrasses, both upper and lower jaws are extremely protrusible, allowing the species to evolve a "sling jaw" that transforms into a long tube to facilitate accurate suction feeding for a variety of prey, including shrimp, crabs, and smaller fishes. When not in use, the jaw, as you note, folds out of the way, under the head.
Slingjaws are reasonably common in depths of 3 to 120 feet over coral reefs in the Indo-Pacific region, from the Red Sea and East Africa east to the Hawaiian Islands and French Polynesia, as far north as southern Japan, and as far south as northern Australia.
Typical of other wrasses, the coloration of this hermaphroditic species varies, with color changes related to the different maturation stages of the life cycle (they mature first as females before turning into males). Smaller juveniles are dark brown with several thin vertical white stripes. This changes to a uniform brown or yellow upon maturation to the "initial phase," so your fish was a female in the dark brown, initial-phase color pattern, Paul. Small groups of females typically occur with one large "terminal phase" male fish, the latter having a distinctive white head with a single diagonal black line through the eye, black flanks with one vertical light green stripe and an orange region below the dorsal fin. If the male is removed from the harem, the next-largest female will soon take its place, changing sex and adopting the terminal-phase color pattern. E. insidiator can grow to around 16 inches long and around 5 pounds in weight. They're known to be quite territorial, with home ranges as large as a quarter of an acre. No slingjaws have been entered for all-tackle record status with the IGFA, so yours could have been the world record!