All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
You must pay the Zakah from this money because it belongs to a Muslim person, reached Nissab (Minimum amount liable for Zakah) and a full lunar year passed over it. You should do so as this is amongst your responsibilities towards your father, in addition to the reward you will receive for paying Zakah on his behalf as this helping him perform an obligatory act of worship. And Allah The Almighty Knows Best .