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UPDATE: I checked the third possible genus that was merged with Machimus/Tolmerus in the past (Neoepitriptus) and indeed is the correct one (spines on front femurs + lack of extension on 8th sternite are considered characters of this genus)! On top of that, I checked the two available keys for the species that I have (Die Fliegen and Asilidae of France) and in both it turned out being N. incostans, a species widespread in the Mediterranean and present in Greece (the white bristles and hairs were indeed a diagnostic character)!

Below, I provide some photos of the external genitalia, which also matched perfectly the avilable figures and descriptions, both in shape and colorations.