Actually, it's the third version
Although the IMDb page for "Farewell, My Lovely" starts out by saying that this is the second adaptation of Chandler's novel, it is in fact the third.
The first was "The Falcon Takes Over". (http://www.imdb.com/title/tt0034716/)
It was made in 1942, two years before "Murder, My Sweet", the second screen version.
Marlowe's name is changed to The Falcon character's name (Gay Lawrence), and he's played by George Sanders!