I recently heard the old complaint of the barking dog. Is this really still too complicated to solve? Here's the solution - Cheerios. Buy a box of Cheerios. Throw a handful of Cheerios over the fence. Was that too fast? I'll say it more slowly. Throw a handful of Cheerios over the fence.
The bark is a warning bark. The dog does not know the intent of, the sound it hears or the sight of the stranger it sees. It is simply warning you off. If you feed the dog it will stop barking. The dog will not warn off food.
Stop shouting at the neighbor, Stop threatening a law suit. Stop demanding obedience school. Damn, try to be smarter than the dog. If you are the dog owner, you buy the Cheerios.
You might even put them in a fruit roll-up. I don't know, get creative.