A family story attached to an object deserves to travel with it when possible.

An object without its story is just an object, and the story lives in a head rather than in the thing. A ring is a ring until somebody says who wore it and when, and then it becomes evidence of a life. When the telling generation goes, the story usually goes too, and what is left is a nice old item nobody can place. Separating the two is how heirlooms quietly become furniture.

Write the story down and attach it to the thing itself. A folded card in the box, three sentences long, keeps a hundred years of context from depending on somebody remembering to say it aloud.