Just a note. The BEA retrieved the fourth seat, but no mention of their retrieving the third seat. This was during the first recovery. (The other two cockpit seats were retrieved with their occupants, and it was the DNA analysis on these two bodies that led the French court to proceed with recovery of other bodies.) One can surmise the BEA may have had an interest in the straps on the fourth seat.
After Ile de Sein swapped crews at Dakar and returned, the second recovery seems to have been dedicated to retrieval of bodies. Looking back, the crew swap may have been to bring on board a team experienced with traumatic death. And it may have been representatives of the French court that were directing the second recovery phase, with the BEA more of an observer.