What is the ruling on making qunut during the morning prayer?

The question of qunut [supplications of morning prayer] is a secondary legal issue that should not be a cause for division and animosity among Muslims. There is a scholarly debate on this issue; the Shafi'is and Malikis said it was preferred, while the Hanafis and the Hanbalis said no supplication are made in the morning prayer.

Al-Nawawi said: "Know that, according to us [i.e. the Shafi'is], [qunut] supplication is legislated in the morning [prayer] and it is an established Prophetic tradition. This is based on the narration of Anas Ibn Malik [who said]: 'The Prophet supplicated in the morning prayer until he left this world.' They [i.e. the Shafi'is] said: “If you neglect to perform it, the prayer is still valid, but you should make the prostration of forgetfulness, regardless of whether its omission was intentional or due to negligence. As for its place [in the prayer], it is occurs after straightening up from bowing in the second cycle of the morning prayer. Supplications made before bowing do not count according to the most correct opinion. You should therefore repeat it after bowing and then make the prostration of forgetfulness."

Different opinions were related by the Prophet’s Companions and their followers concerning the ruling of qunut in the morning prayer. Ali Ibn Ziyad maintained its obligatoriness, such that the prayer of someone who neglects it is invalid. It is permissible to make qunut both before and after bowing in the second cycle, but the preferred position is to make it before bowing after the Quranic recitation without saying 'Allahu Akbar' before it. This is due to the ease it entails for the one who joins the prayer late, the absence of a gap between it and the two integrals of prayer, and because this was what 'Umar used to do in the presence of the Companions. Al-Qadi Abd Al-Wahhab Al-Baghdadi said: "It was related that Abu Raja Al-Atari said, ‘Qunut was made after bowing, but 'Umar made it before bowing so that a latecomer could catch up with the rest.’ It was also related that the Muhajireen [emigrants] and Ansar [helpers] asked 'Uthman about qunut and he made it before bowing, due to the benefit it entails at this position which is the prolonged standing, allowing a latecomer to catch up with the supplications and because the supplications prolong standing, and that which is before the bowing is more deserving of this, especially in the morning prayer."

The Shafi'i position on qunut is the preponderant position due to the strength of their evidence, which is the following:
-What was related by Abu Huraira that: “When the Prophet would raise his head from bowing in the second cycle of the morning prayer, he would supplicate with this prayer, ‘O God, guide us among those You guide…’” Al-Bayhaqi added: “So unto You is praise for what You have decreed” while Al-Tabari added, “None is exalted whom You are at enmity with.”

-The aforementioned hadith of Anas Ibn Malik: "The Prophet made qunut in the morning prayer until he left this world." Anas was asked, "Did the Prophet make qunut in the morning prayer?" He said, "Yes." It was said to him, "Before or after bowing?" He replied, "After bowing."

-Abu Huraira said: "By God, I am the closest of you to the Prophet in prayer." Abu Huraira used to supplicate in the last cycle of the morning prayer after saying, "God hears those who praise Him" and he would pray for the believers, males and females, and curse the disbelievers.

-‘Abdullah Ibn Abbas said: "The Prophet taught us the words to say during the qunut made in morning prayer: “O God! Guide us among those You guide, pardon us among those You pardon, look after us among those You look after, bless us in what You have given us, and protect us from the evil of what You have ordained. Verily, You decree and none decrees against You, and none is abased whom You befriend. You are above all things sacred and exalted.'"

The best words of supplications are those related by Al-Hasan Ibn Ali who said: "The Messenger of God taught me words to say in the witr prayer, “O God! Guide us among those You guide, pardon us among those You pardon, look after us among those You look after, bless us in what You have given us, and protect us from the evil of what You have ordained. Verily, You decree and none decrees against You, and none is abased whom You befriend. You are above all things sacred and exalted.'" Scholars have added the following words, "and none is exalted whom You are at enmity with," which are to be said before "You are above all things sacred and exalted," and after it [they added], "So Yours is the praise for what You have ordained. I seek Your forgiveness and unto You I repent." Al-Nawawi said in Al-Rawdah: "Our companions [i.e. the Shafi'is] said, 'There is no harm in this addition'. Abu Hamid, Al-Bandaniji and others said it is desirable." It is a Sunnah to invoke blessings on the Prophet (peace and blessings be upon him) and his household.
Based on the above, we agree with the position of the Shafi'is in that making qunut in the morning prayer is a Sunnah as it is likewise a Sunnah for someone who misses it to make the prostration of forgetfulness; the prayer is not invalidated by this omission.
And God the Almighty knows best.