9 may 82 shot down by SAM Sea Dart HMS Coventry during rescue of fishing boat Narwall survivors. (1Lt Buschiazzo, Lt Fiorito & Sgt Dimotta killed)
Here is a thought, If you know where it departed from and one assumes they would be more or less be directly tracking towards where the Narwal was hit, which one assumes transmitted its position when attacked, could you not draw a line from the departure point to the ships location and would it not narrow down the search area on the Island? it would be a starting point.
Meanwhile, the Argentine fishing boat Narwal was sailing at 52º 45' S and 58º 02' W, it was attacked by two Sea Harriers, (Fl Lt Morgan and Lt Cdr Batt), with bombs and cannons; then, when some of her crew had abandoned ship, she was boarded by a helicopter, (Lt Cdr Pollok of 846 Sgdn Hermes), and captured by commando personnel. The Narwal sank the next day while she was being towed. Among the prisoners, twenty-five in all, one died, and twelve were injured.
https://www.malvinense.com.ar/smalvi/0109/1084.html
Adding to it, Sadly it appears the Puma came down at sea. From the same article
The Helicopter Puma AE-505 that was shot down when they were going to the place where the fishing boat NARWAL was sinking to rescue the survivors, was shot down by a Sea Dart missile fired from the frigate Coventry on May 9, 1982, the remains of the personnel and The aircraft were not found because they fell into the sea in the vicinity of the Isla de los Leones Marinos. They were decorated with the medal "The Argentine Nation for Valor in Combat" (Post Mortem)