I've done this contract now five times... but only with a smal crane.
The main body part placed (like shown at the screenshot) at the trailer will work fine.
The wing part with engine is the one with the most problems for me (maybe cause the small crane!!!) to fix it at the trailer.
The little wing part I always drive with a flatbed to the airfield (Voron Grad - looked/holded by the crane) there I put it on the trailer to deliver it