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Many thanks for ID, Theo.

Nemorilla maculosa is listed for Fuerteventura.
http://www.azoresbioportal.angra.uac.pt/files/noticias_Lista_Especies_Silvestres_Canarias2010.pdf

I do not collect flies. I only take pictures.

Yes, the host is a micro. There were some leaf wraps either with a caterpillar or with a pupa inside.
The third option was a pupal case and a pupa wrapped together in a leaf.

Marion