I had a great five year relationship with a girl, we lived together and got a dog. Eventually we split up, I kept the dog, she retained rights to see the dog and we stayed on pretty good terms.
I got a new girlfriend a while later and the fact that the ex still took the dog out for walkies once in a while used to drive her nuts. I had no desire to be with the ex at all, our time had passed, but she had been a big part of my life for a while and it would be weird to edit her out of my life to satisfy the whims of someone who was quite unreasonably insecure.
For a quiet life, I eventually revoked the dog walking privileges, ruined my amicable relationship with my ex and only temporarily cheered up my new girlfriend who didn’t last much longer because her insecurities were not limited to exes.
I suppose what I am saying is that it might be you who is insecure and it would do you well to have a very serious think about whether he is really pining for her or just not editing her out of his life for your benefit. We are all made of our experiences and to ask someone to forget or hide their past denies you a lot of insight into who they might actually be.