Between the weakening by Imam al-Nawawi of the saying: (Peace be upon you, and Allah's mercy and blessings) in the closing of the prayer, and the authentication by Ibn Hajar.

The Shaykh : In "Sharh Sahih Muslim" by Imam al-Nawawi, he says - peace be upon him - at the end of the prayer: , and as for the hadith: , it is weak. Is this what Imam al-Nawawi said?
Answer: It is true that Imam al-Nawawi said this, but the one who is more knowledgeable and more established in the science of hadith than Imam al-Nawawi has ruled on the hadith of the salam with the addition of as authentic. When we studied al-Nawawi's weakening of this addition and al-Hafiz Ibn Hajar's authentication of it, the opinion of al-Hafiz Ibn Hajar became stronger in our view. This is not mere following of him, though we have the right to follow him; for he is more knowledgeable than al-Nawawi in hadith. We would have the right to follow him even if we did not know the factor that makes Ibn Hajar's opinion stronger than al-Nawawi's.
So the hadith with the addition of: in the first salam came through two paths. One is from Wa'il ibn Hujr in "Sunan Abu Dawud" with a sound chain, as al-Hafiz Ibn Hajar said, and scientific hadith research confirms this. This hadith also came through another path, other than the path of Wa'il ibn Hujr, which is the path of Abdullah ibn Mas'ud in "Musnad Imam Abu Dawud al-Tayalisi." He is earlier and of a higher generation than Abu Dawud al-Sijistani, the author of "Sunan." Therefore, the coming of the hadith with the addition of: through two paths refutes Imam al-Nawawi's weakening of the hadith and confirms the statement of Imam Ibn Hajar al-Asqalani regarding the authenticity of the hadith.

The questioner : There is a narration ... .

The Shaykh : Yes, in some copies of Abu Dawud, but this copy is the weaker position. The more correct is to restrict it to the first salam, and likewise it came in the corroborating narration I mentioned from the hadith of Ibn Mas'ud in the first salam.