Lots of advice some of it odd. Here is my take.

"She agreed, and these branches (only) were cut, about a month ago"

Good, As it should be.

"However, on returning yesterday from a week away with relatives, she discovered that every other branch had also been cut, and the wood/foliage simply left piled, where it had fallen, in her garden."

Creepy and very bad. Can she prove that the neighbour did it? As you said she can ask the other neighbours. Is there any reason she cannot, in the presence of witnesses ask the neighbour she suspects?

I don't think that the neighbour would get away with saying he had permission. According to the first post He did what he was given permission to do before she went away. The first thing She should do is ask the dude if he cut her tree up. If he says yes, inform him he was trespassing and ask for restitution. Call an arborist and get a quote for the amount. If he says "no" he didn't cut it down, ask the other neighbors if any of them witnessed him (or his agents) doing it if you can't get anyone to step up as a witness, let the matter drop. In any case if he does not agree to restitution, report the incident to the police as an act of vandalism.