I think the "HGF" is actually PGF.
In this thread @François Pépin speculated that PGF was a generic name for a group of casemakers that could have been collectively referred to as Production Générale Française.
In another thread on a different forum, it was speculated that the "G" is not a G at all, but instead is a symbol separating the initials P and F as was commonly done in French hallmarks. For example the manufacturer Pierre Fondary had a hallmark featuring a "fountain" symbol that looked like this:
Not quite a G, but you get the idea. I looked at several different "PF" hallmarks but saw no symbol that I thought looked like a G. Just for giggles I looked for other combinations (PFG, PG, etc) but found nothing of note either.
The HSF mark is hard to read from the picture above. It is likely two initials separated by a symbol, but we need a better image.
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