Ref. No. 1105/42-318
In the name of Allah the most Gracious the most Merciful
The answer to your question is as follows:
Yes, the narration is authentic and recorded in Sahih Al-Bukhari.
عن نافع ان ابن عمر کان اذا دخل فی الصلوۃ کبر ورفع یدیہ واذا رکع رفع یدیہ واذا قال سمع اللہ لمن حمدہ رفع یدیہ واذا قام من الرکعتین رفع یدیہ رفع ابن عمر الی النبی ﷺ۔ (صحیح البخاری باب رفع الیدین اذا قام حدیث نمبر 739)
(Translation: it is narrated by Nafi' that whenever Ibn 'Umar started the prayer with Takbir, he used to raise his hands: whenever he bowed, he used to raise his hands (before bowing) and also used to raise his hands on saying, "Sami a-l-lahu Liman hamida", and he used to do the same on rising from the second Rak'a (for the 3rd Rak'a). Ibn 'Umar said: "The Prophet (Sallallähu Alaihi Wasallam) used to do the same."
And Allah knows best
Darul Ifta
Darul Uloom Waqf Deoband