The only Puma wreck that I am aware of from the conflict is on West Falkland, roughly in the area near Port Howard on a ridge, AFAIR.
IIRC, it was shot down by a Harrier/Sea Harrier. We used to fly over it regularly when I was down there in ‘88.
If your friend identified the other wreck as a Puma, then it sounds as if this is AE-505. 17 Miles is close enough, given the possible confusion that may have occurred during the campaign. Unless anyone positively saw it impacting the water on that day, it almost certainly is your missing Puma