Is it permissible to distribute an inheritance by executing a will of the deceased from the wealth of one of the heirs but not the other, such that one heir receives his full share while the will is deducted from the share of another heir, knowing that this will was not documented in writing or by witnesses?

A will is not accepted unless there is legitimate proof (such as a written document or witnesses). If it is not proven, it holds no weight unless the adult heirs agree to it, because the money belongs to them. If some heirs agree to a will that has no proof, while others do not, then it is to be taken only from the share of those who agree, and the others are not compelled to accept it. However, if all heirs acknowledge the will and wish to have it disbursed from the share of one of them, there is no harm if he is willing and of sound mind. But if he is unwilling or a minor/incapacitated, that is not permissible; for the will is to be disbursed from the estate before it is divided among all heirs. If the deceased bequeathed that the will be disbursed from the share of a specific heir, and it was an unjust bequest, it is not binding on that heir if proof is established against it. In summary: If the heir agrees for the bequest to be disbursed solely from his share, there is no harm. Otherwise, it is to be disbursed from the estate before its division.