Is he guilty?

Sends by means of a public electronic communications network a message or other matter that is grossly offensive or of an indecent, obscene or menacing character or causes such matter to be sent

A person is guilty of an offence if, for the purpose of causing annoyance, inconvenience or needless anxiety to another

Sent by means of a public electronic communications network, a message that he knows to be false

Caused such a message to be sent

Persistently misuseses a public electronic communications network