What is the ruling on items purchased with stolen money after the stolen amount has been repaid, and does this entail a sin? What is the ruling on the sums refunded from returning these purchases? Is there another way to atone for this sin?

If the thief repents, regrets, and returns the stolen goods to their owners, then the repentance is sound and accepted, based on the Almighty's saying: "But whoever repents after his wrongdoing and makes amends, indeed, Allah turns to him in forgiveness. Indeed, Allah is Forgiving and Merciful," and the Prophet's (PBUH) saying: "Regret is repentance." There is no harm in benefiting from items purchased with stolen money after the right has been returned to its owners.