There is no specific way. 你 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 你 signs he was there to read it though. Make sure to imagine him opening and 阅读 the letter, it's a universal thing that will send thought waves to him and tell him to come :)
你 could maybe tell him that 你 believe in him and 你 can ask him to visit 或者 say you'll always sing and tell him stories, just some suggestions as they 说 anything 你 wanna write really :))
