The adulterer is not

Abu Huraira reported: The Messenger of Allah صلى الله عليه وسلم said, “The adulterer is not a believer while he is committing adultery; and the thief is not a believer while he is stealing. However, there is a chance for repentance.”
[Sunan At-Tirmidhi, Book 38, Number 2625, Grade: Sahih]
Book of Faith, Chapter: What is related the adultery not being a believer when he commits adultery

عَنْ أَبِي هُرَيْرَةَ قَالَ  قَالَ رَسُولُ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ لَا يَزْنِي الزَّانِي حِينَ يَزْنِي وَهُوَ مُؤْمِنٌ وَلَا يَسْرِقُ السَّارِقُ حِينَ يَسْرِقُ وَهُوَ مُؤْمِنٌ وَلَكِنَّ التَّوْبَةَ مَعْرُوضَةٌ

قَالَ أَبُو عِيسَى حَدِيثُ أَبِي هُرَيْرَةَ حَدِيثٌ حَسَنٌ صَحِيحٌ