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I don't know if this will help or note but this is the note on Parallelomma in the British checklist.
http://www.dipteristsforum.org.uk/documents/BRITISH_ISLES_CHECKLIST.pdf page 369.

"1. Parallelomma paridis Hering, 1923 was synonymised with vittatum by Šifner (1978), but reinstated by Nelson (1990). Šifner
(1995, 2008) reaffirmed this synonymy, which had not been accepted by Gorodkov (1986), but Nelson's view is accepted here."

I think it comes down to whether you follow Sifner's view that there is only one species or Nelson/Gorodkov that there are two species of Paralleloma.