I am no expert on these but it looks good to me. The colours of the kokarden are correct as well as the use of red and black thread to stitch them on. The weave of the cloth band covering the original red trim looks good and we have nice clear size and Korps ink stamps. An f usually indicates some sort of repairs have been done so the piece is ready for the “field” once again but I don’t see any repairs. My opinion only.
For me also looks good. The VIII. Armeekorps was located in Koblenz, and most of its units were in the "Rhineland" regions (including Cologne).
So also the manufacturer in "Coeln" (today Koeln) fits very well