My mothers fence was fastened to the outbuildings at the bottom of her garden. When the fence fell down she ordered a replacement, but the neighbour who owns the outbuildings asked our builder to stop work because he was planning to demolish them shortly and reduce the height of the wall. We asked the neighbour to pay for the cost of taking the fence down again, but our builder says it’s not worth falling out over.
Take your builder’s advice! At least the neighbour isn’t objecting to your mother attaching a fence to his wall. I imagine it will be cheaper to do this than to put in foundations for the fence posts on your mother’s land, and it would certainly be neighbourly to wait for him to rebuild his wall before putting up the fence.