What is the ruling on purchasing from a teacher's account for a colleague from outside the classroom without his knowledge, and what should be done in this case, and what if it is impossible to reach the teacher?

The permission is specific to the students of the class. Whoever took for someone outside the class, at the expense of the teacher, must inform the teacher and ask for forgiveness, or pay him his due. If he cannot reach him, he should give charity on his behalf, because giving charity for others' rights is not permissible except in cases of inability to deliver those rights to them.