There is no specific way. あなた just write to him. Start slow though and don't rush him with things about yourself. And be patient, he will be very hesitant, and doesn't usually write back. He will leave あなた signs he was there to read it though. Make sure to imagine him opening and 読書 the letter, it's a universal thing that will send thought waves to him and tell him to come :)
あなた could maybe tell him that あなた believe in him and あなた can ask him to visit または say you'll always sing and tell him stories, just some suggestions as they 発言しました anything あなた wanna write really :))
