I first read the issue about it in your first post, then saw the first pic and litterally jumped and yellped a bit..
I *think* from what it appears to be, is plastic resin that most of the RC helmets are made out of. Im not 100% sure on that, but thats what it looks like to me, because thats pretty thin and I dont see fiberglass matt anywhere.
Ive heard of it being able to deform by heat, so I think thats what really happend here. Your going to have to spend a bit of time reshaping this thing. I'd first try fixing those lower cheeks, it's supposed to be straight, not curved. I'd take like a flat wood block, and press it against the inside of it, and use a heat gun to slowly straighten it out, but thats my logic telling me what to do, so I dont know how effective or if that would even work.
I really wish you luck on reshaping this helmet!