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Wow - that looks interesting! In the Red List of Hoverflies of Saxony (https://www.natur...liegen.pdf) as well as the complete list of Germany (https://www.rote-...html#idx_h), the species is considered to be threatened with extinction. To reproduce successfully it needs recently fallen, mature Aspen logs. In the middle picture the female is ovipositing, so this log should remain on its place, which nature conservation workers should ensure.
I think your identification is highly probable, even though Hammerschmidtia and brown Brachyopa species are easily mixed up. In May I saw B. cf. testacea that looked rather similar but not fully identical. According to the key https://www.resea...E-2020.pdf Hammerschmidtia differs from Brachyopa as follows:
- vein R4+5 with apical section longer than crossvein r-m
- hind tibia with short strong black spines on anterior surface
- mesopleural anepisternum, postalar callus, and scutellum with strong bristles
- face of male with tubercle
The wing venation isn't depicted well in your photos, but I see strong bristles on the thorax and, in the middle picture, there might be spines on the hind tibia. Also the tubercle of the male face is visible.
Falk (https://www.flick...382148394/) shows only males, but they look very similar.
You should contact Dieter Doczkal to get an expert opinion and perhaps some advice on where to report and publish this find. If the species is really so rare and endangered, this could perhaps be used to justify the designation of miniature protected area (Flächennaturdenkmal).
Much luck and best wishes, Sundew