The Shaykh’s explanation of the ruling on greeting the one who is praying and the Sunnah regarding how to respond to it during prayer.

The Shaykh : For example, regarding greeting the one who is praying, those who hold that this is disliked have no explicit evidence in the Sunnah, let alone in the Book. They only argue for it based on understanding and opinion, and all of that is open to error. Meanwhile, there are authentic, established hadiths from the Prophet (peace and blessings be upon him) that he was greeted while he was praying, more than once, and that he responded to the greeting offered to him without objecting to it, not once. For example, in Sahih Muslim, there is the hadith of Jabir ibn 'Abd Allah al-Ansari (may Allah be pleased with him) that the Prophet (peace and blessings be upon him) sent him on an errand. When Jabir returned, he found the Prophet (peace be upon him) praying, so he greeted him, and the Prophet (peace and blessings be upon him) responded to his greeting with a gesture of his head. There is another hadith like this one, and it contains another benefit that is not a problem for you to hear. That is the hadith of 'Abd Allah ibn Mas'ud (may Allah be pleased with him), who was one of the Companions who migrated to Abyssinia and was absent from the Prophet (peace and blessings be upon him) for the duration of that time. When he returned, the first time he met the Prophet (peace be upon him), he found him praying, so he greeted him, but the Prophet (peace and blessings be upon him) did not respond to his greeting with words; rather, he also responded with a gesture of his head. 'Abd Allah ibn Mas'ud said, "I was seized by what was near and what was far," meaning that 'Abd Allah ibn Mas'ud began to think, considering things from near and from far. He wondered why the Messenger of Allah (peace and blessings be upon him) had not responded to his greeting, given that he had known before leaving for Abyssinia that the Prophet (peace and blessings be upon him) used to respond to greetings during prayer with words. In the early days of Islam, if someone greeted the one who was praying, he would respond to the greeting with words while praying, and this was a permissible matter. So 'Abd Allah ibn Mas'ud parted from the Prophet (peace and blessings be upon him) to Abyssinia. Therefore, something entered his heart when the Messenger (peace be upon him) did not meet him with the greeting he had been accustomed to receiving from him, namely with words. So he began to think, fearing that he had perhaps made a mistake with the Messenger (peace be upon him) and that He had become angry with him. When the Prophet (peace and blessings be upon him) finished his prayer, and without doubt he knew, either by his intuition or by the inspiration of his Lord, what had occurred in the mind of 'Abd Allah ibn Mas'ud, he said to him, answering what was in his heart: So if the one who is praying is greeted by a man, he responds to the greeting... This indicates that what was previously permissible was then abrogated. Thereupon, the soul of 'Abd Allah ibn Mas'ud was at peace, and he knew that there was nothing related to him, but rather it was... Allah the Exalted reveals what the wisdom of Allah the Exalted requires. So in this hadith, there is also the confirmation by the Messenger (peace be upon him) of the offering of a greeting to him while he is praying, along with the abrogation of the response to the greeting by the one who is praying to the one who greeted him, which had previously been prescribed.
Similarly, it came in Sunan Abu Dawud from the hadith of 'Abd Allah ibn 'Umar that the Prophet (peace and blessings be upon him) visited the Ansar in Quba at their mosque, so they began to come to him in succession. They would meet him while he was praying, and they would offer him the greeting, and he would respond to their greeting with a gesture of his hand. One of the narrators of this hadith described this gesture, saying, "He placed the palm of his hand toward the ground and the back of his hand toward the sky." The Prophet (peace and blessings be upon him), while praying, would be addressed by the one entering the mosque with, "Peace be upon you, O Messenger of Allah," and he would do nothing but do this: "Peace be upon you," raising his hand like this, with the palm of the hand toward the ground and the back of the hand toward the sky. So we take from these hadiths, which are all authentic, praise be to Allah, two things: first, the permissibility of offering a greeting to the one who is praying; second, the obligation to respond to the greeting with a gesture of the hand or the head. This variation by the Messenger (peace be upon him) between gesturing with the hand or the head contains wisdom. That is that gesturing with the head is, without doubt, more appropriate, because it is a movement, whereas raising the hand like this... the one who is praying, when he hears the greeting, feels that he is performing the gesture of the head in place of the gesture of the hand, and he is content with that, because prayer is based on tranquility, calmness, and stillness. Therefore, it is not permissible to fidget in prayer or to perform in it movements that Allah the Exalted has not prescribed through the tongue of His Prophet (peace and blessings be upon him). It was the custom of some of the Companions in the early days of Islam that when they exited the prayer with the taslim, they would wave their hands like this, saying, "Peace be upon you and the mercy of Allah, peace be upon you and the mercy of Allah." So he (peace and blessings be upon him) said to them: the horses, the sun, meaning... the two horses play with their tail, so it resembles these hands when they are raised, like the tail of a horse when it is raised, and they... This means the disapproval of this action, and he confirmed that by saying: Therefore, the principle is that the one who is praying does not perform a movement except out of necessity or by prescription, as we are now in the midst of. So this person greets you, and there are no other people praying around you, for example, so merely doing this makes it understood that you have finished the matter. No, you are among a group, and your response to the greeting by gesturing with the head is not apparent, so at that time you raise your hand, and the raising should also be to the extent that achieves the purpose of the raising, which is to inform the one who greeted you that you have received his greeting and that you have responded to it.