Is it permissible for the agent to continue distributing the annual charity from the money allocated for it after the death of the principal, or must he give the remaining money to the heirs?

The money donated is a charity (sadaqah (definition)), not a bequest (wasiyyah (definition)), and it does not transfer into the ownership of the poor person except after he receives it. If the donor dies before the poor person receives the money that the donor had entrusted someone to deliver, then the money remains the property of the donor and reverts to his heirs. They then have the choice to proceed with the charity or to divide the money among themselves.