On Monday, 19 January 2015 16:50:12 UTC, Phil L wrote:

Bring your side wall in by 6 inches and leave a gap for his extractor to
vent into, will you miss 150mm of space on that side of your kitchen?

Sure it means that he won't be able to access his extractor fan in the
future but that's his problem.

Why not attach a right-angle round to rectangular adapter to his exhaust duct and then bring a rectangular duct out to roof level through your wall cavity as it is being built? He will not lose access to the fan as that is normally in the cooker hood itself. This might solve the problem cheaply and amicably.

You really don't want him to discharge into a narrow gap between the properties as the humidity of the extracted air might cause problems with any timber there.

A separate question is whether he even has the right to discharge into your back garden at all.

John