I had this when i moved in 3 years ago.
I resolved it at the start of this spring by digging up everything in my garden and theirs.
They had told me they had dealt with it but all they had done was strimmered it down to ground level.
The rhizomes had spread for about 6-7metres along the fence line.
It was a mess afterwards and the brown bins were full of roots etc.
The responsibility lies with the neighbour to have their plant correctly contained, preferably in a metal pot which is visible above the ground so the roots can’t jump, trust me they will.
Nothing else will work.