What is the ruling on using public property (such as a phone or printer belonging to a school or charitable organization) for personal purposes, and does the ruling differ between the caller and the recipient?

It is not permissible to use tools without the permission of the authority responsible for them, unless the authority grants permission or if it is customary to do so. As for the recipient of the call, if he knows that the caller is infringing upon the right of another, he is not permitted to receive it, otherwise, he would be a partner in sin, as Allah Almighty says: "And do not cooperate in sin and aggression." If he does not know, then there is no sin upon him.