What can a mother do to ease her conscience after accusing someone of theft and expelling him, then discovering that another thief was the perpetrator, given the difficulty of reaching the wronged person and the long time that has passed since the incident?

The mother's accusation of the worker with theft without verification is forbidden, and it is considered harm to a believer and slander. Allah Almighty says: (And those who harm believing men and believing women for [something] other than what they have earned have certainly borne slander and manifest sin). She must repent and seek forgiveness from the worker, and it is preferable for her to give him money as compensation to mend his feelings.