The quick way to fix this without taking the 4 pound hammer to the anim files is to convert the meshes and reassign all the head type vertices just to the head, of course you lose all facial expresions then - but I did say it was quick, nothing about aesthetics .
Ya, the problem is some part of the helmet is pulled down to his chin.

Thank you, GOM! I'll give it a try.

And what about the complicated way? What shall I do if I don't want to re-assign all head vertices? I don't understand the "90 degree" thing. Could you explain it a little more? Is it about those id, if stats? Thanks in advance!