Is the owner of wealth sinful if he does not pay zakat on his wealth upon which a year has passed and which has reached the nisab, given that the trustee of the wealth knows that he (the trustee) has paid zakat on his own wealth, and that the wealth is intermingled in the trustee's account?

The trustee of money may not dispose of it except with the owner's permission. Zakat (definition) is not obligatory upon him for this money due to his lack of authority over it; zakat is incumbent upon the owner of the money himself. The trustee must advise the owner of the money to pay zakat. If the owner does not comply, the trustee must return the money to him.