Is it permissible for the poor person, who is an agent of funds for the poor and is charged with the upkeep of a religious school, to spend from the agency's funds on the school's teachers?

If a person appoints another to distribute the zakat of his wealth, then it is permissible for the agent to take from that zakat, just as it is permissible for him to give it to anyone who meets the criteria of poverty, whether they are a teacher, an imam of a mosque, or anyone else.