Is it permissible to give a portion of the inheritance as charity with the intention of it being zakat on behalf of the deceased who did not pay zakat during his lifetime, and would that atone for his negligence?

Zakat is an obligatory act and a pillar of Islam, and abandoning it is a grave sin. Zakat is due on what your father left behind, and it is the first thing that should be disbursed from the wealth because it is a debt owed to Allah. Hasten to pay it from the wealth, even if it is for many years, and strive to convince the heirs of this, as it is an act of filial piety towards their father. If they agree, then well and good. If they refuse, and you wish to pay it from your own money, then your action is commendable and rewarded, and it is among the greatest acts of filial piety towards your father and an expiation for his shortcoming. Otherwise, pay the zakat due on your share of the inheritance.