Responding to one who sneezes when he praises Allah

It is narrated from Sayyiduna Abu Hurayrah (may Allah be pleased with him) that two men were sitting with the Prophet (peace and blessings be upon him), one of whom was more distinguished (noble) than the other. The distinguished man sneezed but did not praise Allah, so the Prophet (peace and blessings be upon him) did not respond to him. Then the other man sneezed and praised Allah, and the Prophet (peace and blessings be upon him) said to him 'Yarhamuk Allah' (May Allah have mercy on you). The distinguished man said: I sneezed and you did not respond to me, while this man sneezed and you responded to him? He (peace and blessings be upon him) said: "Indeed, you forgot Allah, so I forgot you; and this man remembered Allah, so I too remembered him."
This hadith has a sahih (authentic) chain of narration, but the two Shaykhs (Bukhari and Muslim) did not record it.

It is narrated from Abu Burdah bin Abi Musa that he said: I was with Sayyiduna Abu Musa (may Allah be pleased with him) while he was in the house of Umm al-Fadl. Umm al-Fadl sneezed and Abu Musa responded to her; then I sneezed and he did not respond to me. I went to my mother and told her, and when Abu Musa came to her, my mother said: My son sneezed in your presence and you did not respond to him, while a woman sneezed and you responded to her? He said: Your son sneezed but did not praise Allah, so I did not respond to him; and she sneezed and praised Allah, so I responded to her. I heard the Messenger of Allah (peace and blessings be upon him) say: "When one of you sneezes and praises Allah, respond to him; and if he does not praise Allah, do not respond to him." At this she said: You have done well, you have done well.
This hadith has a sahih (authentic) chain of narration, but the two Shaykhs (Bukhari and Muslim) did not record it.

It is narrated from Nafi' that a man sneezed in the presence of Sayyiduna Abdullah bin Umar (may Allah be pleased with them both) and said: 'Alhamdu lillahi was-salamu ala rasulillah' (All praise is for Allah, and peace be upon the Messenger of Allah, peace and blessings be upon him). Ibn Umar (may Allah be pleased with them both) said: I too say that all praise is for Allah and peace be upon the Messenger of Allah (peace and blessings be upon him), but this is not how we were taught. the Messenger of Allah (peace and blessings be upon him) taught us that when one of us sneezes, he should say: 'Alhamdu lillahi ala kulli hal' (All praise is for Allah in every state).
This hadith has a sahih (authentic) chain of narration and is gharib (singular) among the biographies of Nafi's teachers, but the two Shaykhs (Bukhari and Muslim) did not record it.

It is narrated from Sayyiduna Abu Ayyub al-Ansari (may Allah be pleased with him) that the Messenger of Allah (peace and blessings be upon him) said: "The one who sneezes should say: 'Alhamdu lillahi ala kulli hal' (All praise is for Allah in every state); the one who responds to him should say: 'Yarhamukumullah' (May Allah have mercy on you); and he (the sneezer) should say to him in reply: 'Yahdikumullahu wa yuslihu balakum' (May Allah guide you and set your affairs right)."
This hadith is among the errors (awham) of Muhammad bin Abd al-Rahman bin Abi Layla, the Ansari jurist and judge (may Allah have mercy on him). Had these errors not appeared, the imams of hadith would not have attributed poor memory to him. The explanation of what I have mentioned is in the next narration.

It is narrated from Sayyiduna Ali bin Abi Talib (may Allah be pleased with him) that the Prophet (peace and blessings be upon him) said: "When one of you sneezes, let him say: 'Alhamdu lillahi ala kulli hal' (All praise is for Allah in every state); let the people say to him: 'Yarhamukumullah' (May Allah have mercy on you); and let him (the sneezer) say: 'Yahdikumullahu wa yuslihu balakum' (May Allah guide you and set your affairs right)."