A "detailed examination" was necessary in the wake of the carbon monoxide results, a lawyer for the family said.
Daniel Machover, of Hickman & Rose solicitors, said: “That dangerously high levels of carbon monoxide have been found in Emiliano’s body raises many questions for the family. How he died will be determined at the inquest in due course. The family believe that a detailed technical examination of the plane is necessary.
"The family and the public need to know how the carbon monoxide was able to enter the cabin. Future air safety rests on knowing as much as possible on this issue.
"Emiliano’s family call on the AAIB to salvage the wreckage of the plane without further delay.”
A previous interim AAIB bulletin on the tragedy confirmed the mystery owner of the plane made no attempts to apply to either American or British authorities for commercial use.
Investigators are still establishing whether the doomed flight took place on a "cost sharing" basis, which does not breach Civil Aviation Authority (CAA) guidelines.
The US-registered Piper Malibu N264DB, unlicensed for commercial flying, fell thousands of feet in the space of 20 seconds after making a 180-degree turn, minutes after Ibbotson requested a descent.