Consider the following premises. There is at least one x for which if x listens to a song, then x is a lawyer. For all x, if x were a lawyer, then x is rich. For all x, x will write a letter if and only if x will listen to a song. Can we infer the following from them? For all x, the fact that x writes a letter does not imply that x is rich.
That contradicts the premises. Therefore the answer is no.