This quest has a bug. I have done this and have the item in my inventory. A guild mate wants to get caught up to me and we ran this quest the day before yesterday and he got nothing. We went on to finish the quest and came back to the area and still nothing. Yes we looted the body and he got nothing. Last night after getting word back from EA we ran it again like they said and it was the same dang thing. The quest is bugged. Not sure how many more times he will be willing to run this before he says to heck with it. With the amount of threads about this EA might want to look into this.
This made me think. I had the bug as well but running the FP second time solved it. But I did read earlier baout other people failing to get HK part even at second attempt.
Did you have the piece in inventory before your friend run the FP the first time? Or were you two picking it in the same FP? Maybe this is what's happening? Your own piece bugs your friend? So the solution would be your friend going without you maybe? (and hopefully no one else in group will just so happen to have the piece too)?