None of us can read minds, and no two people are the same.
I am an alcoholic in recovery and when I break up with someone I'm like you are describing yourself. I get rid of all reminders. I block him and I don't take any contact from him. I don't know how they act after I'm gone or what they keep and I could not care any less! That's part of the "Ex" thing.
It seems to me that his half of the painting is his to do as he wishes. He is free to do whatever he wants and to deal with his memories/his emotions in any way he likes.