[Wardpike]

Remove all hardware and strings. Get some carpenter's (Yellow) glue. you'll also need two pieces of flat smooth hardwood and some clamps. Put some glue in the grooves of the break areas, Line everything up perfectly, put a piece of hard wood on either side with something in between the hardwood and headstock (thin piece of cloth or paper can work) and apply clamps. Clamp it really tightly until most of the glue is forced out. Then wipe off any excess. Leave it to dry for 48 hours. Remove clamps and hardwood (they will want to tick to it all) by tapping the pieces, then clean-up any excess glue and paper/material with a super sharp single-sided razor blade and warm water.

If you line up everything perfectly, you won't even see the crack in the finish.

You also probably signed a waiver with the airline against damages. That's part of their published tariff and I doubt you can claim more than $500. You can sue, but I'd just get the $500, fix the guitar and get a new case.

Next time use an ATA approved flightcase!