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I haven´t seen any of them irl, and I do not have the fly. And the pictures is bad.
Looking at pictures of Graphogaster, it does not look like it, I think. But I don´t know of course.
In real life it really looked like Phasia barbifrons/pusilla. Same size and completely black.

Graphogaster brunnescens can be found from end of June, this was in mid-may.