This hadith has been narrated on the authority of Anas through another chain of transmitters.
Sahih Muslim Book 55, Hadith 70
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So and so sneezed and you said: May Allah have mercy upon you. I also sneezed but you did not utter these words for me. Thereupon he (the Holy Prophet) said: That person praised Allah, and you did not praise Allah.
Sahih Muslim Book 55, Hadith 69 Next Hadith → I visited Abu Musa, as he was in the house of the daughter of Fadl b. 'Abbas. I sneezed but he did not respond to it (by saying): Allah may have mercy upon you. Then she sneezed and he (Fadl b. 'Abbas) said: May Allah have mercy upon you. I came back to my mother and informed her about it, and when he came to her she said: My son sneezed in your presence and you did not say:" Allah may have mercy upon you, and she sneezed and you said for her:" May Allah have mercy upon you." Thereupon he said: Your son sneezed but he did not praise Allah and I did not beg mercy of Allah for him and she sneezed and she praised Allah and so I said: May Allah have mercy upon you, as I heard Allah's Messenger (ﷺ) as saying: When any one of you sneezes he should praise Allah and the other should say: May Allah have mercy upon you, and if he does not praise Allah, no mercy should be begged for him.
Sahih Muslim Book 55, Hadith 71
Sahih Muslim Book 55, Hadith 69 Next Hadith → I visited Abu Musa, as he was in the house of the daughter of Fadl b. 'Abbas. I sneezed but he did not respond to it (by saying): Allah may have mercy upon you. Then she sneezed and he (Fadl b. 'Abbas) said: May Allah have mercy upon you. I came back to my mother and informed her about it, and when he came to her she said: My son sneezed in your presence and you did not say:" Allah may have mercy upon you, and she sneezed and you said for her:" May Allah have mercy upon you." Thereupon he said: Your son sneezed but he did not praise Allah and I did not beg mercy of Allah for him and she sneezed and she praised Allah and so I said: May Allah have mercy upon you, as I heard Allah's Messenger (ﷺ) as saying: When any one of you sneezes he should praise Allah and the other should say: May Allah have mercy upon you, and if he does not praise Allah, no mercy should be begged for him.
Sahih Muslim Book 55, Hadith 71