I suppose whoever paid for the post is ultimately its owner whichever side of the boundary it is on. Its like someone kicking a football into your garden you cannot claim it and it remains the property of whoever bought it, your not obliged to throw it back or do anything with it or even allow a person on your property to claim it.

I would have a word with your neighbour and explain the situation as you have here he seems reasonable having already replaced the post for you. What you do not want is a boundary dispute they do not end well for either party with only the lawyers making money out of it. A couple of inches here or there especially where it does not really matter is not worth getting worked up about.

Drilling through the post and using nuts & bolts is by far the best option, aim for the centre the rebar tends to be more in the corners.

Richard