Emiliano and pilot David Ibbotson are both now missing, presumed dead, after their plane went missing two weeks ago.
This is an active investigation now in the hands of the AAIB (Air Accidents Investigation Branch), and they will be taking over as agreed.
It was revealed on Monday that wreckage of the plane carrying the pair had been found in the English Channel, following a privately funded search.
"Tragically in video footage, one occupant is visible amid the wreckage".
Shipwreck hunter David Mearns, who led the £300,000 GoFundMe search, said: "I've been in touch with Emiliano's family and they desperately want the aircraft recovered".
Sala's sister Romina shared the image of his rescue dog Nala staring out into the distance.
Mr Mearns said he was in regular contact with the family.
No timeframe has been set to decide whether to recover the wreck of the plane carrying Emiliano Sala and David Ibbotson, investigators have said.
However, Ross Taylor, whose A-2-Sea survey ship was used to pinpoint the location of the plane said recovery could prove hard with the remote vehicle and using divers would be "a much bigger operation".
A body was later discovered by the wreckage, but it is yet to be identified.
"It cleared the immediate area for the Geo Ocean III to use its underwater remotely operated vehicle (ROV) to survey the area of the seabed in which the object was located".
"As tragic as the loss is, it's made much, much worse if the body is never recovered or (the family) never get an answer to what happened", Mearns said. Sala was on his way to the Welsh capital to train with his new teammates for the first time after completing a£15 million ($19 million) move to Cardiff City from French side Nantes on January 19.
He said "I communicated with the search party every day". "Divers can also get down to that depth but it's a much bigger operation".
Mr Mearns, who has spearheaded around 20 historic wreck discoveries including one of Britain's most famous battleships the HMS Hood, said with the right equipment it should be a relatively straightforward job to lift the plane.
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