Literary detective whose final case is in 1975's "Curtain"

POIROT

This Belgian sleuth with a distinctive mustache often relies on his "little grey cells" and first appeared in a 1920 novel set on a train.

This clue points to Hercule Poirot, the famous Belgian detective created by Agatha Christie. His last recorded case appears in the 1975 novel Curtain, where he solves a murder at Styles Court—the same setting as his first mystery. The name "Poirot" fits the answer directly, with no wordplay or hidden meanings involved.