I saw the Messenger of Allah ﷺ raising his hands apposite the shoulders at the time of beginning the prayer and before bowing down and after coming back to the position after bowing. but he did not raise them between two prostrations.  

رَأَيْتُ رَسُولَ اللَّهِ ﷺ إِذَا افْتَتَحَ الصَّلاَةَ رَفَعَ يَدَيْهِ حَتَّى يُحَاذِيَ مَنْكِبَيْهِ وَقَبْلَ أَنْ يَرْكَعَ وَإِذَا رَفَعَ مِنَ الرُّكُوعِ وَلاَ يَرْفَعُهُمَا بَيْنَ السَّجْدَتَيْنِ  

Ibn Umar reported that the Messenger of Allah ﷺ, when he stood up for prayer, used to raise his hands apposite the shoulders and then recited takbir (Allah-o-Akbar), and when he was about to bow he again did like it and when he raised himself from the ruku' (bowing posture) he again did like it, but he did not do it at the time of raising his head from prostration.  

كَانَ رَسُولُ اللَّهِ ﷺ إِذَا قَامَ لِلصَّلاَةِ رَفَعَ يَدَيْهِ حَتَّى تَكُونَا حَذْوَ مَنْكِبَيْهِ ثُمَّ كَبَّرَ فَإِذَا أَرَادَ أَنْ يَرْكَعَ فَعَلَ مِثْلَ ذَلِكَ وَإِذَا رَفَعَ مِنَ الرُّكُوعِ فَعَلَ مِثْلَ ذَلِكَ وَلاَ يَفْعَلُهُ حِينَ يَرْفَعُ رَأْسَهُ مِنَ السُّجُودِ  

This hadith has been transmitted with the same chain of transmitters by al. Zuhri as narrated by Ibn Juraij (who) said. When the Messenger of Allah ﷺ stood up for prayer, he raised hands (to the height) apposite the shoulders and then recited takbir.  

ابْنُ جُرَيْجٍ كَانَ رَسُولُ اللَّهِ ﷺ إِذَا قَامَ لِلصَّلاَةِ رَفَعَ يَدَيْهِ حَتَّى تَكُونَا حَذْوَ مَنْكِبَيْهِ ثُمَّ كَبَّرَ  

Abu Qilaba reported that he saw Malik b. Huwairith raising his hands at the beginning of prayer and raising his hands before kneeling down, and raising his hands after lifting his head from the state of kneeling, and he narrated that the Messenger of Allah ﷺ used to do like this.  

أَنَّهُ رَأَى مَالِكَ بْنَ الْحُوَيْرِثِ إِذَا صَلَّى كَبَّرَ ثُمَّ رَفَعَ يَدَيْهِ وَإِذَا أَرَادَ أَنْ يَرْكَعَ رَفَعَ يَدَيْهِ وَإِذَا رَفَعَ رَأْسَهُ مِنَ الرُّكُوعِ رَفَعَ يَدَيْهِ وَحَدَّثَ أَنَّ رَسُولَ اللَّهِ ﷺ كَانَ يَفْعَلُ هَكَذَا  

The Messenger of Allah ﷺ raised his hands apposite his ears at the time of reciting the takbir (i. e. at the time of beginning the prayer) and then again raised his hands apposite the ears at the time of bowing and when he lifted his head after bowing he said: Allah listened to him who praised Him, and did like it (raised his hands up to the ears).  

أَنَّ رَسُولَ اللَّهِ ﷺ كَانَ إِذَا كَبَّرَ رَفَعَ يَدَيْهِ حَتَّى يُحَاذِيَ بِهِمَا أُذُنَيْهِ وَإِذَا رَكَعَ رَفَعَ يَدَيْهِ حَتَّى يُحَاذِيَ بِهِمَا أُذُنَيْهِ وَإِذَا رَفَعَ رَأْسَهُ مِنَ الرُّكُوعِ فَقَالَ سَمِعَ اللَّهُ لِمَنْ حَمِدَهُ فَعَلَ مِثْلَ ذَلِكَ  

This hadith has been transmitted by Qatada with the same chain of transmitters that he saw the Messenger of Allah ﷺ doing this (i.e. raising his hands) till they were opposite the lobes of ears.  

أَنَّهُ رَأَى نَبِيَّ اللَّهِ ﷺ وَقَالَ حَتَّى يُحَاذِيَ بِهِمَا فُرُوعَ أُذُنَيْهِ