Is it permissible to give some brothers copies of the Qur’an that have been donated to the mosque?

If the Qur'ans are endowed for the mosque, then it is not permissible to give them to any other person, unless there is a significant surplus not needed by the mosque's attendees, and there is someone who needs some of them. In such a case, there is no harm in giving him what he needs to achieve a benefit. If it is possible for it to be a loan, then that is obligatory.