I'm not to sure about this.
Fasche:
ist die Bezeichnung für eine rahmenartige Einfassung aus z.B. Stein, Putz oder auch Holz.

Molding:
Milled trim piece that covers the gap between the window frame and exterior finish.
Casing:
Trim moulding applied around interior and exterior window and door openings to
cover the gap between the frame or jamb an the wall.
molding:. An embellishment in strip form, made of wood or other structural material, that is used to decorate or finish a surface, such as the wall of a room or building or the surface of a door or piece of furniture.

Thank you for your reply.

May be I am wrong, but I think, "moulding/casing" does not hit the point. It seems to describe something like "Blendrahmen" or even "Zierleiste"

The german word "Fasche" does not mean something that covers the gap between windowframe and masonry.
Often the "Fasche" consists of a narrow border (approx. 2cm) in the external plaster directly placed at the edge of the reveal, which is painted in the same color as the reveal itself.

Die Fasche als Zierelement von Gebäuden gibt es im englischen Sprachraum nicht so häufig. Es ist daher wahrscheinlich schwierig, ein passendes Wort zu finden. Ich habe mal unter "Einfassung" nachgesehen und entscheide mich für "edging".