My Daddy Long Legs Episode 34 (1990)

Judy Abbott is an orphan living in New York, who at the age of 17 finds herself in receipt of a college scholarship and monthly allowance from a mysterious benefactor. Her benefactor believes she has great potential as a writer and wishes to see her succeed. The only payment he asks in return is that she write him a letter every month addressed to the pseudonym "Mr. John Smith," with the understanding that he will never reply.