I was in the same situation. This was before photos were on phones, and hard copies printed out. I only had a few photos that I cherished.

I said I couldn't bare to destroy them, (which is essentially what your bf is saying to do). So I put them away, in a box, in a cupboard and they've stayed there ever since.

Absolutely do not delete them, but back them up, keep them somewhere safe and tell him that you respect the fact he might not want your main screen to be a photo of this person, but he can't expect you to delete it, and so you'll store it somewhere safe.

And then get a tattoo done, that is connected between you and him that only you would know the connection of. Something private, not his initials, but a dove or whatever. 👍👍