Whenever the Messenger of Allah ﷺ stood for prayer, he would raise his hands until they were level with his shoulders, then say the takbir while they were in that position, then bow. When he wished to lift his back up, he would raise his hands until they were level with his shoulders, then say, "Allah hears whoever praises Him." He did not raise his hands in prostration, but he raised them with every takbir he pronounced before bowing, until his prayer was complete.
حدثنا محمد بن المصفى الحمصي حدثنا بقية حدثنا الزبيدي عن الزهري عن سالم
كان رسول الله ﷺ إذا قام إلى الصلاة رفع يديه حتى تكون حذو منكبيه ثم كبر وهما كذلك فيركع ثم إذا أراد أن يرفع صلبه رفعهما حتى تكون حذو منكبيه ثم قال سمع الله لمن حمده ولا يرفع يديه في السجود ويرفعهما في كل تكبيرة يكبرها قبل الركوع حتى تنقضي صلاته
Sourcing, sahih. Daraqutni narrated it, 1/287, no. 1098, from the hadith of Baqiyyah with this chain. Ibn Zuhri's nephew narrated it from Zuhri with this chain, recorded by Ahmad, 133/2, 134, and Ibn Jarud, no. 178, and its chain is sahih.