Is it permissible to seek forgiveness for a father who lived as an atheist, and it was said that he uttered the Two Testimonies at the time of death, even though the one who said so is not trustworthy in his truthfulness?

Prompting a disbeliever to utter the Two Testimonies (Shahadatayn) at the time of death is a good act and a form of inviting them to Islam, just as the Prophet, peace and blessings be upon him, did with his uncle Abu Talib and his Jewish servant. The disbeliever should be prompted to say both testimonies: "There is no god but Allah, Muhammad is the Messenger of Allah," along with the word "I bear witness," because one does not embrace Islam without both. This prompting is obligatory if there is hope of their embracing Islam, and recommended if there is no such hope. If you strongly believe that your father died upon Islam, then it is permissible to seek forgiveness for him. However, if it is established or strongly believed that he died upon disbelief, then it is not permissible, by consensus, to pray for mercy or forgiveness for him.