Strangers in the Night (1944)

A lonely, mentally unbalanced woman invents a fictitious daughter and has the "daughter" write to a Marine stationed in the South Pacific. When the soldier returns back to the States, he goes to look up his pen pal, and is told by the "mother" that the daughter has moved away. An acquaintance of the women tells the soldier the truth, and in a rage the "mother" kills her. In order to cover up that crime, she realizes she must kill the soldier, too.