Change a prefab's sprite in all scenes?

I'm having some trouble right now with my player sprite. I have a little shop inside my game where you can change the skin of the player, i've used a sprite changer script:

 public class SpriteChanger : MonoBehaviour
 {
     SpriteRenderer spriteRenderer;
     // Use this for initialization
     void Start()
     {
         spriteRenderer = GetComponent<SpriteRenderer>();
     }
     public void change(Sprite differentSprite)
     {
         spriteRenderer.sprite = differentSprite; 
     }
 }
 

It works fine inside the shop, but when i change from my Shop Scene to my Game Scene (i have a back to menu button, then a play button) It is not saved, even though I'm using the same player prefab on both the shop and the game scene. What do you think is the problem? I haven't really seen any tutorial addressing this error.