I'm not an expert but my understanding is that the sailor has to request his own leave through his command
He must submit a special request chit to his chain of command, with the desired dates and a basic itinerary on it to his chain of command. They approve it in a week or two, or they deny it. How far in advance depends on his command.
But no, no one but the sailor themselves can request leave. It is odd he doesn't know this.
You sure he's not in prison and requesting you petition for him?