Must the heirs pay zakat on behalf of their deceased father, who did not pay zakat for two years before his death, knowing that he used to send money to his needy brothers in Palestine? And will paying it benefit him after his death?

If your father owned zakatable wealth that reached the nisab (minimum threshold) in that year, then zakat on it is obligatory, and his inability to work does not prevent its obligation. Zakat must be disbursed from the inheritance before its distribution, as zakat is a debt owed to Allah, and He has the most right to be paid, in accordance with His saying, the Most High: ﴿after any bequest he may have made or any debt﴾, and the hadith: "The debt owed to Allah is more deserving of being fulfilled." This is obligatory whether the deceased bequeathed the zakat or not. As for the money your father sent to Palestine, it is not considered zakat unless he intended it as zakat at the time of disbursement.