Dear God (1996)

Tom Turner is a con man, defrauding people from their money with a variety of two-bit hustles. One night he makes the mistake of attempting to hustle some undercover cops, and finds himself in court faced with the dilemma of either going to jail or getting a real job. Choosing to stay out of jail, he gets a job at the post office working in their Dead Letter Office helping to sort Dead Letters (i.e. mail which, for whatever reason, can't be delivered). Some of the mail he receives can't be delivered because it's addressed to God, and he accidentally answers (sending them money in the process). This starts the ball rolling as more of his co-workers get in on the idea of helping people by answering "God" mail.