Is the money left by a brother with his [other] brother — with him saying to him, "This money is yours if I die" — considered a right of the deceased brother, or is it a trust, and what should be done with a trust after its owner's death?

The statement "It is yours upon my death" is a gift conditioned on death and takes the ruling of a will. If you are not an heir to your brother, then the money is yours if it does not exceed one-third of his estate. If it exceeds one-third, you only take one-third, and the remainder goes to the heirs, unless they consent. If the heirs dispute you, evidence must be presented (one man and two women, or one man and the claimant's oath). If evidence is not presented, the money belongs to the heirs, and what you have given as charity, you are liable for and must return its equivalent to them. Trusts must be paid to the heirs of their owner after his death.