The supplication for completing the Qur'an is well known among the Salaf

Q: What is the ruling on the supplication for completing the Qur'an?

A: The Salaf have always completed the recitation of the Qur'an and read the supplication for the completion in the Ramadan prayer, and we are not aware of any disagreement among them regarding this. Therefore, the most likely ruling in such a case is that it is read, but it should not be prolonged for the people. One should seek out beneficial and comprehensive supplications, such as what Aisha (may Allah be pleased with her) said: "The Prophet (peace and blessings be upon him) preferred comprehensive supplications and left aside what was other than that."
Therefore, it is best for the imam in the supplication for completing the Qur'an and in the qunut to seek out comprehensive words and not to prolong things for the people. He should recite: which was reported in the hadith of al-Hasan regarding the qunut, and add to it whatever easy, good supplications are available, as 'Umar added. He should not strain himself, not prolong things for the people, and not make it difficult for them. Likewise, in the supplication for completing the Qur'an, he should supplicate with whatever easy, comprehensive supplications are available. He should begin that with praising Allah and sending blessings upon His Prophet (peace and blessings be upon him), and conclude it in whatever is available of the night prayer or in the witr. He should not prolong things for the people in a way that harms them and makes it difficult for them.
This is well known from the Salaf; the later generations received it from the Salaf, and so our shaykhs did, with their seeking of the Sunnah and their care for it. They did so, with the last of them receiving it from the first, and it is not hidden from the imams of the da'wah who seek the Sunnah and strive for it.
The conclusion is that there is nothing wrong with this, if Allah wills, and there is no blame on him; rather, it is recommended. This is because it involves seeking to respond to supplication after reciting the Book of Allah . Anas , when he completed the Qur'an, would gather his family and supplicate outside of prayer. It is the same in prayer, for the principle is one: supplication is prescribed in prayer and outside of it, and the type of supplication is what is prescribed in prayer, so it is not objectionable.
And it is known that supplication in the prayer is required when reading the verse of punishment, and when the verse of mercy, a person supplicates at that point, as the Prophet (peace and blessings be upon him) did in the night prayer. So this is like that, prescribed after completing the Qur'an. The discussion is only if it is inside the prayer. As for outside the prayer, I am not aware of any disagreement that it is recommended to supplicate after completing the Qur'an. But in the prayer, that is where the excitement and research have occurred now. I do not know of anyone from the Salaf who denied this inside the prayer, just as I do not know of anyone who denied it outside the prayer.
This is what is relied upon in that it is a matter known among the Salaf, which the first of them and the last of them practiced. So whoever says: "It is reprehensible," he must provide the evidence, and it is not upon the one who did what the Salaf did. Rather, establishing the evidence is upon the one who denied it and said: "It is reprehensible" or "It is a religious innovation (bid'ah)." This is what the Salaf of the Ummah practiced and proceeded upon, and their Khalaf received it from their Salaf. Among them were scholars, the righteous, and hadith scholars. And the type of supplication in the prayer is known from the Prophet (peace and blessings be upon him) in the night prayer; so this should be of the same type as that.