I’d worry that the older son would not feel obligated to keep the painting in the family. If it is a gift, which he thinks it was, then he is free to do with it what he wants. If he bought it (and pays for it), then he can do with it what he wants.
The only way it can remain in the family permanently is if younger son still owns it and it is merely on loan to the older son. That doesn’t seem to be anyone’s view of the transaction (it was either a gift or should have been a purchase).
I think ownership should be sorted out sooner rather than later. Older son’s girlfriend may think it is theirs. A future wife might think it is theirs and subject to division with martial property.