I would say in my opinion, this is a made up item. Gangsters obviously modified violin cases for Thompsons, but they wouldn't go to all the trouble of having various little compartments. To accept all the different bits & Bobs!
I mean the front grip is held on with a screw. WHY would they take both grips along on a job in the same case? They wouldn't have time waiting 'on a job'. To unscrew the horizontal front grip screw, & remove the grip. Then locate the long screw for the vertical grip & then fit that.
The whole purpose of the case, was to disguise & carry the weapon to it's deployment location. Then quickly whip it out & (Generally) fit the 50 round mag & use the Gun.
From reports I have read from official sources, on Gangsters of that era. A VAST amount of them could NOT shoot accurately with handguns!
Also, quite a lot of them were not the brightest of individuals either!....They didn't have the nouse in a lot of cases, to think too deeply. About the technical aspects of their chosen 'Profession'!...The 'act first, without thinking it all through' scenario. Was quite common.
This is one of the major reasons the Thompson was the weapon of choice, for gangsters. Not being good shots, the 'spraying' technique of full-auto Guns.
Was a better option for them then! The Police only took them on strength as well, so as to be on a 'level playing field' so to speak. It evened things up for them.
I believe SOME cases were modified officially. But this was more for novelty value, than tactical. Auto-Ordanance did indeed make purpose designed transit cases for Thompsons. But there were recqtangular in shape, with a folding handle on the hinging lid.