It is narrated from the Messenger of Allah ﷺ that whenever he stood to perform the obligatory prayer, he would say the takbir and raise his hands level with his shoulders. He would do the same when he finished his recitation and was about to bow, and he would do it again when he rose from bowing. He would not raise his hands at any point during his prayer while he was seated. When he rose from the two prostrations, he would likewise raise his hands and say the takbir.
عن رسول الله ﷺ أنه إذا قام إلى الصلاة المكتوبة كبر ورفع يديه حذو منكبيه، ويصنع مثل ذلك إذا قضى قراءته، وإذا أراد أن يركع، ويصنعه إذا رفع من الركوع، ولا يرفع يديه في شيء من صلاته وهو قاعد، وإذا قام من السجدتين رفع يديه كذلك وكبر.
Abu Dawud (744), Tirmidhi (3423), and Ibn Majah (864) all narrated it through the route of Sulayman bin Dawud Hashimi, who said, Abdul-Rahman bin Abu Zinad narrated to us, from Musa bin Uqba, from Abdullah bin Fadl bin Rabia bin Harith bin Abdul-Muttalib, from Abdul-Rahman Araj, from Ubaydullah bin Abu Rafi, from Ali bin Abu Talib, who related the hadith in the same manner, and the wording given here is that of Abu Dawud. As for Tirmidhi, he included with it the opening supplication which will come in the chapter on what has been reported about the Prophet's ﷺ supplication during the two pauses after the takbir, which Muslim narrated through another route via Abdul-Rahman Araj. Tirmidhi said, "Hasan sahih." Ibn Khuzayma also graded it sahih, narrating it (584) through the route of Ibn Abu Zinad.I say, its isnad is hasan because of Abdul-Rahman bin Abu Zinad. Ajli deemed him trustworthy, and Ibn Adi said, "He is one whose hadith is written down," while Ibn Main declared him daif, saying, "He is nothing." Zaylai transmitted in Nasb Raya (1/412), from the author of Imam, who said, "I saw in Ilal Khallal, from Ismail bin Ishaq Thaqafi, that Ahmad was asked about this hadith of Ali, and he said, 'Sahih.'" And he said, regarding the statement "and when he rises from the two sajdahs" that it means the two rakahs. End of quote.On this subject there is also what was reported from Anas bin Malik, "that the Messenger of Allah used to raise his hands when he entered the prayer, and when he bowed in ruku." In another narration, "when he raised his head from ruku, and when he prostrated." Ibn Majah (866) and Daraqutni (1119) narrated it from the hadith of Abdul-Wahhab Thaqafi, from Humayd, from Anas, who related it. But Daraqutni found fault with it, holding it to be a stopped report. Likewise Tirmidhi transmitted in his Ilal (1/219) the same view from Bukhari. See for more Fath al-Bari by Ibn Rajab (4/326), where he confirmed that flawed hadiths have been reported concerning raising the hands at sujud and elsewhere.But this does not preclude that the Prophet ﷺ did that once or twice, as mentioned before, except that he did not persist in it, so it seems his final practice was to leave off raising the hands at sujud, at rising from it, and between the two sajdahs. For this reason Tahawi and others claimed there is consensus that one should not raise the hands between the two sajdahs.Likewise, what was reported from Abu Musa Ashari is not sound as a raised report. He said, "Shall I show you the prayer of the Messenger of Allah ﷺ?" So he said the takbir and raised his hands, then said the takbir and raised his hands for ruku, then said, "Allah hears whoever praises Him," and raised his hands, then said, "Do it like this," and he did not raise his hands between the two sajdahs. Daraqutni narrated it (1124) through the route of Ishaq bin Rahawayh, who said Nadr bin Shumayl informed us, who said Hammad bin Salama narrated to us, from Azraq bin Qays, from Hattan bin Abdullah, from Abu Musa Ashari, who related it. He then narrated it through another route from Zayd bin Hubab, from Hammad bin Salama, with his isnad, from the Prophet ﷺ, in similar wording, and said, "These two raised it as a raised report from Hammad bin Salama, while others made it a stopped report from him."I say, by "others" he means Ibn Mubarak, for he narrated it from Hammad bin Salama and made it a stopped report attributed to Abu Musa. Bayhaqi narrated it through this same route, as the Shaykh (that is, Ibn Daqiq Eid) said in Imam. See Nasb Raya (2/415).Bayhaqi, in the chapter on raising the hands at ruku and at raising the head from it, in the second volume of his Sunan (p. 68), mentioned the hadith of Ibn Umar, Malik bin Huwayrith, Waail bin Hajar, Abu Humayd Saadi, Abu Bakr, and Ali bin Abu Talib, but he did not mention there the hadith of Abu Musa Ashari, whether raised or stopped. Rather, he stated explicitly that the hadith was raised to the Prophet ﷺ from Abu Musa Ashari, Jabir bin Abdullah Ansari, Abu Hurairah, and Anas bin Malik, from the Prophet ﷺ. So consider where he actually placed it.After Bukhari narrated in his treatise Raf al-Yadayn (1) the hadith of Ali bin Abu Talib through the route of Ibn Abu Zinad, he said, "It is likewise reported from seventeen individuals among the companions of the Prophet ﷺ that they used to raise their hands at ruku and at rising from it, they are Abu Qatada Ansari, Abu Usayd Saadi Badri, Muhammad bin Maslama, Sahl bin Saad Saadi, Abdullah bin Umar bin Khattab, Abdullah bin Abbas, Anas bin Malik the servant of the Messenger of Allah ﷺ, Abu Hurairah Dawsi, Abdullah bin Amr bin As, Abdullah bin Zubayr bin Awwam Qurashi, Waail bin Hajar Hadrami, Malik bin Huwayrith, Abu Musa Ashari, Abu Humayd Saadi Ansari, Umar bin Khattab, Ali bin Abu Talib, and Umm Dardaﷺ." End of quote.Bayhaqi said in his Sunan (2/75), after mentioning Bukhari's statement, "We have also narrated from these, and from Abu Bakr Siddiq, Umar bin Khattab, Ali bin Abu Talib, Jabir bin Abdullah Ansari, Uqba bin Amir Juhani, and Abdullah bin Jabir Bayadi."I say, among these were those who were present with Abu Humayd Saadi when he prayed in the manner of the Messenger of Allah's ﷺ prayer. Among them were Abu Qatada, Harith bin Rubai, Muhammad bin Maslama, Sahl bin Saad, Abu Usayd, and others.Then know that the hadith on raising the hands at the takbir of ihram, at ruku, and at rising from it is transmitted through so many chains that it is mutawatir from the Prophet ﷺ. Iraqi mentioned in Taqrib al-Asanid that it is reported from fifty of the companions, including the ten who were given glad tidings of Paradise. End of quote. Except that this includes narrators of raising the hands at the opening only, so Shawkani and others hold that the narrators of raising the hands at ruku and at rising from it number approximately twenty.Uzai said, "This is what the scholars of Hijaz, Sham, and Basra agreed upon." Bukhari said, "It is narrated by a number of the people of Hijaz, Iraq, Sham, Basra, and Yemen." Muhammad bin Nasr Marwazi said, "We do not know of any region whose people altogether abandoned raising the hands at lowering and rising in prayer, except the people of Kufa, for all of them raise their hands only at ihram." See Tarh al-Tathrib (2/252–255).In what we have mentioned of the hadiths of some of these companions, there is sufficiency in place of the hadiths of others which are not free of criticism, though it has not been established from any of the companions of the Prophet ﷺ, as Bukhari said, "that he did not raise his hands, and its chains of transmission are not more sahih than those for raising the hands," Juz Raf al-Yadayn (p. 166). He also said, "In what we have mentioned there is sufficiency for whoever understands it, if Allah wills," (p. 106).He also narrated through the route of Ibn Ajlan, who said, I heard Numan bin Abu Ayyash say, "Everything has an adornment, and the adornment of prayer is that you raise your hands when you say the takbir, when you bow in ruku, and when you raise your head from ruku" (p. 152). See for more Minna Kubra (1/492).Bukhari's statement, "its chains of transmission are not more sahih than those for raising the hands," is an indication rebutting what Ibn Abu Shayba narrated (1/236) from Abdullah bin Masud, Ali, and their companions, and what others narrated from Ibn Umar, that they did not raise their hands except at the first takbir of the prayer. In his statement there is a clear indication that the hadiths affirming the practice take precedence over the hadiths denying it.