Complex sentence: McCadden, having figured out that the "mummy" is an alien and having made the connection between the alien and the crystals, then traces the stolen crystals back to Sharpe, who admits to the theft and gives McCadden the fifth crystal.
Split into simpler sentences: McCadden, having figured out that the "mummy" is an alien, makes the connection between the alien and the crystals. He then traces the stolen crystals back to Sharpe, who admits to the theft and gives McCadden the fifth crystal.