The Messenger of Allah ﷺ said, "Whoever stands in prayer during Ramadan out of faith and in hope of reward will be forgiven his past sins."
قال وقال رسول الله ﷺ من قام رمضان إيمانا واحتسابا فإنه يغفر له ما تقدم من ذنبه
Its isnad is sahih. Bukhari related it in 3/33, in the Book of Fasting, chapter of whoever fasts Ramadan out of faith. Muslim related it in 1/523, number 759, in the Book of the Prayer of Travelers, chapter on encouraging the night prayer of Ramadan. Abu Dawud related it in 2/49, number 1371, in the Book of Prayer, chapter on the night prayer of the month of Ramadan. Tirmidhi related it in 3/163, number 808, in the Book of Fasting, and said, hasan sahih. And Nasai related it in 3/201, number 1602, in the Book of the Night Prayer, chapter on the reward of whoever performs the night prayer of Ramadan.