I understand what you mean and how you are reasoning it. The first thing of course is to check that the items mark is corresponding to the correct masters mark, control mark and the city mark. It is also true that Gratchev had masters working for it during that period. However there is no indication in literature that I know of, that there would have been a master AH working for Gratchev which is a first red flag.
The mark on the shown item has been machine carved/casted from an authentic one and there are several indications of it. A machine carved mark is shallow with thin letters. Also there are irregularities in sharpness/straightness of the letters and the marks edges. In comparison a stroked mark has very sharp details, letters and edges which is very difficult to fake.
The last killing factor is that even the spelling of Gratchev on the fake mark is wrong. Most probably who ever did the fake mark didn't even know the Russian language. Nothing one would expect from an Russian state control officer.
I have seen these fake marks also before during my long time as a collector. I found one more Gratchev mark to show in addition of those shown by you from literature. If you look and compare yourself these following two pictures you can see the differences.
