I’m sorry your neighbour has gone down this route. It’s not only destructive to the rat but also anything else that may eat it or the rat
If the rat can get into your garden it’s very likely the hedgehog can get into theirs.
The hog is unlikely to eat the rat but it will eat the poison
I suggest you ask your neighbour to put the poison into something too small for the hog to get into, and that also they remove it as soon as they’ve got rid of the rat