Your Character Blueprint is inherited from Character and the “Add Movement Input” is function that is found from Pawn. Character is descendant of Pawn so the function is also available to Character BP. When you copy and paste your nodes to Player Controller the “Add Movement Input” function disappears because it does not exist on the Controller (since it does not inherit from Pawn). If you want to pass the input values from Controller to your Character you have to “Get Controlled Pawn” (or something like that) on your Controller and use it to pass the values to the Pawn.
Hope this helps, unfortunately I’m not on my development machine so I can’t show the node setup in image form.