What is the ruling on money earned by a father from cutting tree branches from the forest to feed sheep, and then selling them, while knowing that the Water and Forest Authority prohibits this? Is it permissible for the son to benefit from this money, knowing that he does not work and has no other money?

The state's prohibition of cutting trees and grazing livestock falls under the category of restricting permissible acts. If this restriction serves a benefit or if violating it leads to harm, then the one who violates it is sinful. However, the price of the sheep does not become unlawful, and there is no harm in benefiting from the aforementioned money. It appears that the questioner is afflicted with waswasah (obsessive whispering).