I added a music controller to my mod and when I change the song from it and close the mod, it goes back to the previous song.
The music is changed in the screen "mp3", that is included in the screen "Caracters", that is included in the screen "caractergame_menu" that itself looks like a screen opened from the main menu.
You are changing the music at the main menu context level. The change you make is only valid as long as Ren'Py stay in that context, or in any lower context level created
after that change. But when you close the screen, you leave that context and return to a lower context created
before the change. What make the music fall back to what was previously played.
The "mp3" screen should only be available directly from the game context, either by being directly available from the UI, or by opening (as normal modal screen) through a button available from the UI.