Not a "hard information" but a thought for further searching:
I think his name could have been SCHIER.
SHEER in english sounds like the german name SCHIER.
SHEER would be spoken in german like SHARE in english, which would be written SCHÄR, SCHAER or SCHEER.
So if he came to Britain and said "my name is Schier" and the listeners heard SHEER, then that's what he was probably called from then on.
HENRY was probably originally HEINRICH, so when searching in Germany, keep an eye out for these possible variations, in particular HEINRICH SCHIER
Bob