Abu Huraira said that God’s Messenger used to commend prayer at night in Ramadan, but did not command it as a duty. He would say, “If anyone prays during the night in Ramadan because of faith and seeking his reward from God, his former sins will be forgiven him.” When God’s Messenger died this was the practice, and it continued thus during Abu Bakr’s Caliphate and the early part of ‘Umar’s. Muslim transmitted it.
Source: sunnah.com
Other translations
Arabic
وَعَنْ أَبِي هُرَيْرَةَ رَضِيَ اللَّهُ عَنْهُ قَالَ: (كَانَ رَسُولُ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ يَرْغَبُ فِي قِيَامِ رَمَضَانَ مِنْ غَيْرِ أَنْ يَأْمُرَهُمْ فِيهِ بِعَزِيمَةٍ فَيَقُولُ: «مَنْ قَامَ رَمَضَانَ إِيمَانًا وَاحْتِسَابًا غُفِرَ لَهُ مَا تَقَدَّمَ مِنْ ذَنْبِهِ. فَتُوُفِّيَ رَسُولُ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ والمر عَلَى ذَلِكَ ثُمَّ كَانَ الْأَمْرُ عَلَى ذَلِكَ فِي خِلَافَةِ أَبِي بَكْرٍ وَصَدْرًا مِنْ خِلَافَةِ عمر على ذَلِك» . رَوَاهُ مُسلم
sunnah.com