Eric Frank Russell's "Venturer of the Martian Mimics" aka "I, Spy" aka "Spiro" (novelette, detective, free): Exploits of a Martian spy on earth
There is no mystery for reader, though. We see the alien land & shapeshift in the first scene itself. Still a good read; I finished it in a single sitting.
Fact sheet.First published: Tales of Wonder, #12 (Autumn 1940).
Download full text as part of scans of the Weird Tales, May 1947 (Canadian Edition) where it was reprinted.
Related: Stories of Eric Frank Russell (annotated & ranked list).