What should I do with a sum of money I borrowed from a Christian maid and have not repaid her after her departure, and is it permissible to give its value in charity on her behalf?

Effort must be made to deliver the maid's right to her. If that is not possible, then you should give the money in charity on her behalf. If she is found later, she is given the choice between affirming the charity or receiving the money. If she accepts, then that is it; otherwise, you pay her what is due to her, and the reward for the charity will be yours. The evidence for this is a fatwa from the Permanent Committee regarding lost money belonging to a Christian, which stated that it is obligatory to search for the rightful owner, and if that is not possible, then the money should be given in charity with the intention on behalf of its owner. If the owner appears, they are informed of what was done. If they do not approve, their right is paid to them.