How can one atone for stealing money in childhood, given that the exact amount is unknown and the owner cannot be informed? Is continuous charity and sincere repentance sufficient for this?

Repentance from theft is not complete except by returning the stolen amount to its owners, provided the thief is capable of doing so. If the exact amount is unknown, the thief must estimate it with due diligence, ensuring the amount returned is likely to cover the stolen sum or even exceed it. It is not a condition to inform the owner of the theft; rather, it is sufficient to restore the right to them by any means.