Is it permissible for the Imam to execute a non-Muslim child captured during war?

Primary text

If the Imam captures unbelievers, it is not permissible to kill a child who has not reached puberty, and this is without dispute. Evidence for this is the narration of Ibn Umar, wherein the Prophet, peace and blessings be upon him, forbade the killing of women and children. Furthermore, a captive child becomes a slave upon capture, so killing him constitutes the destruction of wealth. If a child is captured singly, he becomes a Muslim, and his killing is the destruction of one who could potentially become a Muslim.