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Oh - and I was so happy that Moschweb http://www.tachin...chweb.aspx led me directly to Exorista... Obviously I lost Phryxe when clicking "frontal setae, on parafacial, reaching the mid of the facial ridge" and "setae on facial ridge above vibrissa robust and more or less erect". However, comparing the excellent photo series of Steven Falk on Exorista (https://www.flick...234307197/) and Phryxe (https://www.flick...234296337/), I feel that Moschweb's alternatives are not entirely unambiguous...
The head profile of Phryxe is obviously not as angular as that of Exorista, it is more rounded and better matching my fly. So with the key https://tachinida...igures.pdf I arrived at P. vulgaris or P. heraclei. I tend to the latter because it is rather dark and the dusting of the tergites is less extensive, but of course the name has to include a "cf."!
So thank you for pointing out further options.