Old black and white doppelganger movie

I saw it about 30 years ago. Involved a man who has a family and then finds out that he has a double who eventually takes over his life and family. A specific scene where he always breaks his match when he lights a cigarette and his double does the same. Movie is in black and white. The style is Hitchcock. In the final scene in the rain the main character goes to his house to get his family back but they and the double reject him.

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