I disagree. If you look at the drawing, you can see a small part of the original thin line indicating the boundary, where the free-hand drawn thick line wobbles a little. The thin line it seems and to some extent the free-hand line, go down the centre between the two house walls. That would seem to suggest that his neighbour is already over the boundary with the right hand side of his gate. The edge of that garden retaining wall visible next to the gate in the photo, the retaining wall is built entirely on the OP's property. That leaves me wondering who built and owns that retaining wall?
Both leaves of the new wall are entirely built on the OP's land.
The dog-legged part of the new wall, close to the road, would seem to be approximately where it ought to be and had it been continued straight back without the dog-leg, it would have been an accurate indication of the boundary. His present wall in its entirety between the two building has been entirely built on the OP's land.
I would guess his neighbour has made a slight boundary land grab in the distant past and is now claiming a much bigger slice of the once shared access space between the houses.
oh yes, I see what you mean re the wobble - I stand corrected, but I guess the op is now into territory where there has already been a change in the boundary at some point in history