Hi Jetski.
When you look out your back door, as you face down towards the rear of your garden is the fence on your right or left hand side ?
If it is on your RIGHT side then the onus is on you to replace, or repair.
If it is on your LEFT side then the onus is on your neighbour to replace or repair.
Neighbours are tricky mate, some are good, some are bad.
I waited for my neighbours to go on holiday, and pushed the fence into their garden, I then rang the Police and said I saw somebody in the neighbours garden at 3am, when the neighbour came back off holiday, he received a Police report letter, and I told him that I thought someone was trying to break in, and the fence was a security issue.
New fence put up in a week- job done.
Remember : It's not what you do, its how you do it !