If a man breaks up with a woman and kicks her out...who should keep the engagement ring?

My ex boyfriends ex (to whom he was engaged) wants the paperwork for her ring which she still has posession of so she can sell it. He doesnt want to give it to her because he took the time to pick it out and it was specially for her… her kids even helped to make it special and unique. What do you think should happen with the ring and should he give her the paperwork to it so she can sell it? Oh and what is the “proper” amount to be spent on a wedding ring anyway? Does it have to do with the annual income?