Cousin Lied To Funeral Home And Said My Grandfather Had No Descendants

(Texas and Arkansas) My father has not been in contact with his father since his father got out of prison in the late 80s. While trying to help my dad look for his father this weekend, I accidentally discovered that he passed away literally last week. My dad reached out to the funeral home to find out if there would be a funeral, and they were shocked to hear from him, as they had been told by my dad's cousin that he had no children or any other living family members. This is entirely untrue, as he is survived by a son (my dad) and a daughter. We live in Texas, his father lived and died in Arkansas. We don't know if he had a will or anything. What steps can my dad take to see if he and his sister have any inheritance?

The funeral home said they would give my dad's contact info to the cousin who paid for the cremation.... But I have a feeling the cousin will not reach out and may actively fight our involvement. A few months ago my dad tried to contact his father through that cousin to let him know that his other son, and that exact cousin lied and said he didn't know who he was talking about, and lied about an address trying to redirect my dad to look somewhere else.