BABY FACE MORGAN(1942)
In the set: 100 Greatest Mystery Classics

A different kind of crime story! The main man
of the gang world kicks the bucket and the rest of
the underworld decide they need a replacement! So
they get the bright idea of getting his son to take
up where his father left off! The main problem: the
son has no idea what his dad did! So he turns the
underworld upside down when he starts an honest
business of actual insurance instead of the
protection racket! B+

A review from IMDb.com:

After "Central City" loses its mob boss to murder,
partner-in-crime Robert Armstrong (as "Doc" Rogers)
decides to take drastic measures To preserve criminal
continuity, he recruits the dead mobster's milquetoast
son, Richard Cromwell (as Edward "Baby Face" Morgan),
to run the family business. The naive Mr. Cromwell
is taken to the city, and installed as President of
his father's "Acme Protection Agency", a front for
gangsters. While Cromwell sells innocently sells
insurance, his "employees" run an extortion racket.
Cromwell falls for pretty client Mary Carlisle
(as Virginia Clark); and, the duo find themselves
in great danger… "Baby Face Morgan" catches star
Cromwell and Ms. Carlisle nearing the end of their
once "promising" film careers. It's a quick,
light, and inoffensive little crime drama.

**** Baby Face Morgan (9/15/42) Arthur
Dreifuss ~ Richard Cromwell, Mary Carlisle,
Robert Armstrong - wes-connors