What is the ruling on women giving men ijazah (licence to teach) in Qur’an or academic texts?
Question

Is it permissible for a woman to give a man ijazah (licence to teach) in Qur’an or academic texts?
Praise be to Allah.Women’s historical role in the Islamic sciences
In the history of the Islamic sciences, women have played a major role. It is sufficient for us to note the Mother of the Believers, the scholar and devoted worshipper ‘A’ishah bint Abi Bakr. How much knowledge she taught and conveyed.
Ibn al-Qayyim (may Allah have mercy on him) said: ‘A’ishah was prominent among those who had knowledge of the shares of inheritance, shar‘i rulings, and halal and haram. Among those who learned from her – who would not give precedence to any view over hers and who acquired great knowledge from her – were al-Qasim ibn Muhammad ibn Abi Bakr, her brother’s son, and ‘Urwah ibn az-Zubayr, the son of her sister Asma’.
Masrooq said: I saw the prominent ones among the Companions of the Messenger of Allah (blessings and peace of Allah be upon him) asking her about the shares of inheritance.
‘Urwah ibn az-Zubayr said: I never talked with anyone who was more knowledgeable about the settling of issues between people in accordance with Islamic law, stories from the time of Jahiliyyah, or poetry, or who was more knowledgeable about the shares of inheritance and medicine, than ‘A’ishah."(A‘lam al-Muwaqqi‘in  2/39).
After the Mother of the Believers ‘A’ishah, there appeared other great female scholars. Al-Hafiz Ibn Hajar wrote a biography of Zaynab bint al-Kamal, who was a famous scholar of hadith who never married. He said: She passed the age of ninety, and with her death, the people lost a great deal of hadith knowledge."(Ad-Durar al-Kaminah  2/209).
Ibn Kathir wrote a biography of Sutaytah bint al-Qadi al-Husayn al-Mihamili, in which he said: She learned the Qur’an and studied fiqh (jurisprudence), the shares of inheritance, arithmetic, Arabic grammar, and so on. She was one of the most knowledgeable people of her time regarding the Shafa‘i madhhab."(Al-Bidayah wa’n-Nihayah  12/321).
Al-Hafiz Ibn al-Jawzi mentioned in Manaqib al-Imam Ahmad the men from whom Imam Ahmad narrated hadith, and he did not mention any women except Umm ‘Umar bint Hassan ibn Zayd ath-Thaqafi.
Ibn Kathir said in al-Bidayah wa’n-Nihayah (18/140): On the Day of ‘Arafah, the righteous shaykhah and devoted worshipper Umm Zaynab Fatimah bint ‘Abbas ibn Abi’l-Fath ibn Muhammad al-Baghdadiyyah died on the outskirts of Cairo, and many people attended her funeral. She was one of the great female scholars; she enjoined what is right and forbade what is wrong, and she opposed the Ahmadiyyah sect for their [illicit] friendship with women and beardless youths; she criticised their conduct and that of the people of innovation (bid‘ah) and others. By doing that she was about to achieve what men were unable to do. She used to attend the majlis of Shaykh Taqiy ad-Din Ibn Taymiyah and learned that from him and others. I heard Shaykh Taqiy ad-Din praise her and describe her as virtuous and knowledgeable. It was reported that she had memorised a great deal or most of al-Mughni, and that he [Shaykh Taqiy ad-Din] would prepare himself for her visits, because she would ask many questions; she asked good questions and was quick to understand. She is the one who taught the Qur’an from beginning to end to many women, including my wife’s mother, ‘A’ishah bint Siddiq, who was the wife of Shaykh Jamal ad-Din al-Mazzi, and she is the one who taught Qur’an to her daughter, my wife Amat ar-Rahim Zaynab. May Allah have mercy on them all and honour them with His mercy and His paradise. Ameen. End quote.
Women from whom men narrated hadith
In their biographies of female scholars, the scholars have mentioned the men and others who narrated from them, of whom we may mention the following:
In the biography of Fatimah the daughter of the Messenger of Allah, it says that her son al-Husayn, ‘A’ishah, Umm Salamah, Anas and others narrated from her. Siyar A‘lam an-Nubala’ (Rashidun – 50).
Umm Salamah the wife of the Messenger: Sa‘id ibn al-Musayyab, Shaqiq ibn Salamah, al-Aswad ibn Yazeed, ash-Sha‘bi, Abu Salih as-Samman, Mujahid, Nafi‘ ibn Jubayr ibn Mut‘im, her freed slave Nafi‘, Nafi‘ the freed slave of Ibn ‘Umar, ‘Ata’ ibn Abi Rabah, Shahr ibn Hawshab, Ibn Abi Mulaykah and many others narrated from her. As-Siyar (2/202).
Hafsah bint Sirin Umm al-Hudhayl al-Faqihah: her brother Muhammad narrated from her, as did Qatadah, Ayyub, Khalid al-Hadhdha’, Ibn ‘Awn and Hisham ibn Hassan. As-Siyar (4/507).
Fatimah bint al-Hasan ibn ‘Ali al-Baghdadi al-‘Attar: Abu’l-Qasim ibn as-Samarqandi, the Qadi of al-Maristan, ‘Abd al-Wahhab al-Anmati and Abu Sa‘d ibn al-Baghdadi narrated from her. As-Siyar (18/480).
In the biography of ar-Ru‘ayni al-Gharnati Abu Ja‘far, it says that he studied ash-Shatibiyyah under Fatimah bint al-Yunayni, as she had received ijazah to teach it from al-Kamal ad-Darir."(Ghayat an-Nihayah 1/151).
In the biography of Ibrahim ibn Abi ‘Ulbah, it says that he received learned recitation from Umm ad-Darda’ as-Sughra Hujaymah bint Yahya al-Awsabiyyah. He said: I recited the Qur’an to her seven times."(Ghayat an-Nihayah  1/19)
Ruling on women giving ijazah to men
Conclusion:
There is nothing wrong with a woman who has memorised the Qur’an well and is proficient in recitation giving ijazah to men in knowledge of Qur’an or any branch of knowledge in which she is proficient, especially if she is an older woman, very old, and there is no fear of temptation by her or for her.
And Allah knows best.