The signature of "Remember to be happy in the future" can be written to yourself. Because I was unhappy a while ago, I urge myself to say goodbye to my former self. I must be strong and happy in the future and don't let troubles haunt me.
You can guess it's addressed to you, but it may be a romantic misunderstanding.
The point is that even if he doesn't write to you, an unhappy person will remind himself to be happy. If you can't let go and want to make it back, just do it. It's only been half a month since we broke up. He must be in the pain of loneliness, and there is still a chance to recover.