I think he's kept it. Not somewhere out in the open, as I doubt he could bear to look at it, but hidden away. I don't think he'd get rid of it. Going by his letter, he did love Molly (or at least he thought he did), but whether that continued after she left is hard to say. At the very least, there has to be some bitterness. But, I don't think he can let go completely, so I think it's maybe stored in a box somewhere.