Nice find. It looks to be in pretty nice condition still. Thanks for sharing.
I don't doubt that it could have been found in a field in it's original box but that hardly makes it an "imfamous gangster gun". It may have been stolen in it's original box and stashed or dumped in a field. But by the looks of the box, you can bet that it's wasn't in a field long. SE Michigan has high humidity and even the summer morning dew would have detroyed that box in a short time.
Not too many criminals carry their working guns around in boxes. Hard enough to hide a gun, let alone the box.
The Purple Gang, as most criminals in the Motor City, are known to dispose of their "used guns" in the River as it was very hard to locate anything in the Detroit River in those days. Still quit a task as the river has a heavy current and poor visability.
Theres a nice example of a Purple Gang Thompson machine gun in the Michigan State Police Crime Lab in Sterling Heights Michigan which was fished out of the river. For some reason the Purple Gang marked some of their guns with a P G. Not really a smart move, even back then.