Is it permissible to ask for mercy for a deceased non-Muslim woman, and to recite Al-Fatiha or other parts of the Quran for her soul?

Whoever dies without having recited the Shahada (testimony of Islam), it is not permissible to supplicate for mercy for them or seek forgiveness for them. The Prophet, peace and blessings be upon him, was forbidden from seeking forgiveness for his uncle Abu Talib, despite his defense of him, because he did not utter the Shahada and died upon the religion of Abd al-Muttalib. Based on this, it is not permissible to supplicate for mercy for the aforementioned woman who died in a state of polytheism (shirk), nor to recite the Quran for her soul. Sheikh al-Islam stated that it is not permissible to seek forgiveness for disbelieving parents unless they embrace Islam, as Allah the Almighty says: "It is not for the Prophet and those who have believed to ask forgiveness for polytheists, even if they were relatives."