Johnny Quintana was only 31 when he died Thursday of an apparent heart attack.
He had wanted to have a second child with his fiancee, Gisela Marrero, but the only way to make it happen was to quickly collect his sperm, which stays fresh for only 36 hours after death.
A court order was needed because Quintana and Marrero were not yet married.
The Bronx judge said "yes" Friday with only four hours left until the deadline.
Sperm bank staffers then rushed to Jacobi Medical Center, where Quintana's body lay.
Marrero already has a 2-year-old son with Quintana.
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