Posted: 23/02/2016 at 09:00
Id speak with the neighbour first, see if they can put a barrier in the ground to prevent roots coming into your property. Maybe even offer to help them do this?
If they refuse, and don't seem to care about you and your problem then I'd dig a deep trench in your boarder along the fence line so you can see any roots growing through, and cut them.
If after a year or two the problem persists then I'd still consider poisoning the roots on your side of the garden boundary. Enough time will have passed to disassociate you from the death of your neighbours plant.
If the neighbours plant dies then tough luck on them for not taking steps to prevent the problem. But speaking to your neighbours should be the first step.