Narrated Abu Huraira: Allah's Messenger (ﷺ) said, "Whoever prayed at night the whole month of Ramadan out of sincere Faith and hoping for a reward from Allah, then all his previous sins will be forgiven." Ibn Shihab (a sub-narrator) said, "Allah's Messenger (ﷺ) died and the people continued observing that (i.e. Nawafil offered individually, not in congregation), and it remained as it was during the Caliphate of Abu Bakr and in the early days of 'Umar's Caliphate."
Source: sunnah.com
Other translations
Arabic
حَدَّثَنَا عَبْدُ اللَّهِ بْنُ يُوسُفَ، أَخْبَرَنَا مَالِكٌ، عَنِ ابْنِ شِهَابٍ، عَنْ حُمَيْدِ بْنِ عَبْدِ الرَّحْمَنِ، عَنْ أَبِي هُرَيْرَةَ ـ رضى الله عنه ـ أَنَّ رَسُولَ اللَّهِ صلى الله عليه وسلم قَالَ " مَنْ قَامَ رَمَضَانَ إِيمَانًا وَاحْتِسَابًا غُفِرَ لَهُ مَا تَقَدَّمَ مِنْ ذَنْبِهِ ". قَالَ ابْنُ شِهَابٍ فَتُوُفِّيَ رَسُولُ اللَّهِ صلى الله عليه وسلم وَالأَمْرُ عَلَى ذَلِكَ، ثُمَّ كَانَ الأَمْرُ عَلَى ذَلِكَ فِي خِلاَفَةِ أَبِي بَكْرٍ وَصَدْرًا مِنْ خِلاَفَةِ عُمَرَ ـ رضى الله عنهما.
sunnah.com