For how many years is the Zakat due on money left by the deceased who did not pay Zakat on it during his lifetime, and how is this Zakat calculated from the remaining amount?

Your grandfather's heirs must pay zakat (definition) from his wealth if he died without having paid it, because it is a debt owed to Allah. Zakat is to be paid for all the years he did not pay it, whether few or many. If they are unsure about the number of years, they should err on the side of caution (for instance, by counting three years instead of two). The amount disbursed as zakat does not factor into the calculation for the following year's zakat; rather, zakat is paid on the remaining amount after deducting the previous year's zakat.