Here's a later episode of Humphrey Bogart and Lauren Bacall's radio show, Bold Venture.
Bogart played the owner of a small Havana hotel (and owner/skipper of a boat that he would charter). Bacall played his ward/friend/employee Sailor Duval.
Bold Venture ran for a season and a half from 1951-52. It was a top notch show, but didn't run on a network (it was syndicated). Despite not having a network to back it the show was still very successful and only ended when Bogart lost enthusiasm for doing the show. (His work schedule plus two young kids took up most of his time.)
The interesting thing about Bold Venture is that the episodes go by different names. This one is commonly known as, "Sailor's Dead Husband," but may actually have been titled, "Sailor is a Wealthy Widow."
Some stations aired Bold Venture out of order, and many of the episodes may be lost (although new ones are found every now and then in the collection of a fan who had a tape recorder back in the 50's).
Here is, "Sailor's Dead Husband," aka, "Sailor is a Wealthy Widow."