I would have suggested that the telegram is the direct object, and therefore it should be the subject of the passive sentence: A telegram will be sent ... with the sender and recipient in either order.
One day when I'm dead and have a chance to have my "explain the mysteries of the universe" conversation with ***, one of my questions will be "Why, oh WHY do people learning English have this unholy fascination with unnatural passive constructions that no native would ever say?" This is a mild one compared to some of them!
I think that the fascination is more on the side of the teachers than the students. It makes a fine theoretical exercise in sentence manipulation, but does it actually help the students, or hinder them?