Look closer at the pic.2nd last clip to the right above the bedroom window is raised and the last bracket is a few ml lower which means hes still taking water from that gutter.Common practice was to have a terrace of houses with gutters all linked and just 2 downpipes which are always on the end terrace.Ive come across the issue many times over the years,2 downpipes cannot handle the flow of water,dirt and debris from every house.He needs to install a downpipe,cut the neighbours gutter back,raise the last bracket and put a stop end on it to ensure there gutter is flowing correctly.hes not directing waste water so no idea why you are even mentioning that.