Poe Dameron was the original owner of the jacket that Finn later sported.
Outerwear, specifically jackets, served as a type of clothing designed to be worn as an additional layer on the torso. In preparation for his wedding to Leia Organa, Han Solo received a jacket from his acquaintance Lando Calrissian. Calrissian falsely claimed the jacket originated from Organa's homeworld of Alderaan to persuade Solo to wear it.