If it is impossible to return money to its owners, is it sufficient to donate it with the intention that it be an expiation for the sin? And is it permissible for a mother to complete the donation with the intention of expiation for her son’s action?

The question has already been answered, stating that the questioner is not obliged to give in charity what he earned, but rather he is obliged to guarantee the rights of the software owners and compensate them for what they missed due to his use of the unlicensed version. His assumption that they might use the money for unlawful purposes is not to be taken into consideration.

If the questioner is unable to return their rights to them, it is permissible for him to spend it on public welfare and charitable causes. There is no harm in his mother donating that amount or a part of it on his behalf, provided it is done willingly on her part.