If the fence is yours, then it’s really up to you to sort it. When we moved in to our present home, the fence between us and elderly widow next door was very rickety, it was hers, but she didn’t own the property, it was step daughter’s, she was just allowed to live there for her lifetime.
She said she wasn’t doing anything about the fence, but we could replace it if we wanted, which we did.
Yes, it benefits both sides to have a decent fence, but if he doesn’t want to contribute, up to him.
You can always ask though, he might share the cost.
Army horses loose on London streets