Answered by our Shaykh, the 'Allāmah, the Trustworthy Advisor, Abu 'Abdirrahmān Yahya bin 'Ali Al-Hajūri - may Allāh preserve him - on the 9th, Sha'bān, 1442H
Question: The one who is forgiven, are his sins erased from his scrolls?
Answer: Yes, they are erased, if Allāh forgives him, he erases them for him.
(يَمْحُوا۟ ٱللَّهُ مَا يَشَآءُ وَيُثْبِتُۖ وَعِندَهُۥٓ أُمُّ ٱلْكِتَٰبِ)
"Allāh blots out what He wills and confirms (what He wills). And with Him is the Mother of the Book (Al-Lawh Al-Mahfūdh)"
[Ar-Ra'd, 39]
(فَأُو۟لَٰٓئِكَ يُبَدِّلُ ٱللَّهُ سَيِّـَٔاتِهِمْ حَسَنَٰتٍۗ وَكَانَ ٱللَّهُ غَفُورًا رَّحِيمًا)
"For those, Allāh will change their sins into good deeds, and Allah is Oft-Forgiving, Most Merciful."
[Al-Furqān, 70]
So they are erased. His statement 'forgive', it (means) covering and erasing and removing.
(قُلْ يَٰعِبَادِىَ ٱلَّذِينَ أَسْرَفُوا۟ عَلَىٰٓ أَنفُسِهِمْ لَا تَقْنَطُوا۟ مِن رَّحْمَةِ ٱللَّهِۚ إِنَّ ٱللَّهَ يَغْفِرُ ٱلذُّنُوبَ جَمِيعًاۚ إِنَّهُۥ هُوَ ٱلْغَفُورُ ٱلرَّحِيم)ُ
"Say: "O 'Ibādi (My slaves) who have transgressed against themselves (by committing evil deeds and sins)! Despair not of the Mercy of Allāh, verily Allāh forgives all sins. Truly, He is Oft-Forgiving, Most Merciful."
[Az-Zumar, 53]
And the black thawb is more concealing of stains, so it includes covering and erasing.