Does my brother have the right to claim half of my money, which I deposited with him for twenty years, under the pretext of managing it, knowing that he previously acknowledged that it was entirely my money?

The issue can be understood in two ways:

First: That the money was sent as a deposit for safekeeping, and the brother then invested it without the owner's permission. In this case, the principal must be returned immediately. As for the profit, the preferred opinion is that it belongs to the owner of the deposit, because the action of the trustee is considered the action of an usurper.

Second: That the expatriate brother authorized his brother to manage his money. If a known fee was stipulated, the agent is entitled to it. However, if no fee was stipulated and he declared it as a voluntary act (تبرع), he is not entitled to anything. If there was silence regarding a fee or a voluntary act, then custom is considered. If the agent is someone who works for a fee, then he is entitled to a customary fee (أجر المثل); otherwise, he is not entitled to anything unless the principal willingly grants it.