Is it permissible to ask Allah that the sum of $225, which was given in charity, be an expiation for a sum of $8 taken fraudulently from a friend to whom the money cannot currently be returned, knowing that the money was taken without knowledge of its unlawfulness, and is that considered a sin?

Lying is forbidden (haram), and taking money from a friend without her knowledge by misappropriating a trust is void (batil). The path to repentance is to return the money to its owner. If it is impossible to reach her, then one should give it as charity on her behalf. If the owner of the money appears and approves of the charity, then that is sufficient. Otherwise, the money must be returned to her. The intention to gift the reward (thawab) of the previously given charity to the owner of the money is not sufficient.