Some massive recovery ship with crane capable of 500,000lb lifting capacity arrives on-site
Actually weight is really insignificant compared with other deep sea recoveries; it is only 250 short tons. More significant is the size.
If they do recover the fuselage to near the surface then a lift not that difficult.
Whole destroyers and frigates have been brought home on barges. IIRC HMS Nottingham was one and USS Cole another.