How should one act who has taken money through illicit means and wishes to return it, given that the total amount is unknown, the currency value has changed, and the owner of the money has passed away?

The person who took the money must accurately estimate the amounts he took and return them precisely to the heirs of the deceased employer, even if they are wealthy. It is not permissible for him to give the money in charity on behalf of the deceased as long as the heirs exist. If he fears exposure, he must deliver the money to them by any means.