//JMenu favorites = new JMenu("Favorite songs");
favorites = new JMenu("Favorite songs");
The Favorites menu needs to be defined as a class variable. Then when you do this your ActionListener can now reference the menu and add a new menu item to the menu.
if (cmd.equalsIgnoreCase("Favorite song")) {
Music.f.add(Music.s);
System.out.println(Music.s + " added to favorites");
System.out.println(Music.f + " current list");
JMenuItem item = new JMenItem(...);
favorites.add( item );