The "H" is going to be the last name of the mechanic that either worked the action or filled the frame. Hard to say with just a single initial but it could be for one of the Hengelhaupt boys, one of the Helfricht folks or some other craftsman in Suhl with the last name beginning with a "H". I don't think it would be for Heym, but the possibility exists.

Kind Regards,

Raimey
rse