How can i save a sprite with FileStream

I have this code that creates shops that can interact with each other. Basically I want to save which items are in which shops (lists). However when i tried to use FileStream I couldn't save the sprites from the items. Anyone could help?

 using System.Collections;
 using System.Collections.Generic;
 using UnityEngine;
 using UnityEngine.UI;
 using System.IO;
 using System.Runtime.Serialization.Formatters.Binary;
 
 [System.Serializable]
 public class Item
 {
     public string itemName;
     public Sprite icon;
     public float price = 1f;
 }
 
 public class ShopScrollList : MonoBehaviour {
     public List<Item> itemList;
     public Transform contentPanel;
     public ShopScrollList otherShop;
     public ShopScrollList otherShop2;
     public ShopScrollList otherShop3;
     public ShopScrollList otherShop4;
     public Text myGoldDisplay;
     public SimpleObjectPool buttonObjectPool;
     public float gold = 20f;
     public int shop2 = 0;
     public int shop3 = 0;
     public int shop4 = 0;
     public Button backbutton;
 
     // Use this for initialization
     void Start () {
         RefreshDisplay ();
 
         if (System.IO.File.Exists ("save.dat")) {
             using (Stream stream = File.Open ("save.dat", FileMode.Open)) {
                 var bformatter = new System.Runtime.Serialization.Formatters.Binary.BinaryFormatter ();
                 List <Item> itemList = (List<Item>)bformatter.Deserialize (stream);
             }
         }
 
     }
 
     public void RefreshDisplay()
     {
         myGoldDisplay.text = "" + gold.ToString ();
         RemoveButtons ();
         AddButtons ();
     }
 
     private void AddButtons()
     {
         for (int i = 0; i < itemList.Count; i++) {
             Item item = itemList [i];
             GameObject newButton = buttonObjectPool.GetObject ();
             newButton.transform.SetParent (contentPanel, false);
 
             SampleButton sampleButton = newButton.GetComponent<SampleButton> ();
             sampleButton.Setup (item, this);
         }
     }
 
     private void RemoveButtons()
     {
         while (contentPanel.childCount > 0) {
             GameObject toRemove = transform.GetChild (0).gameObject;
             buttonObjectPool.ReturnObject (toRemove);
         }
     }
 
     public void TryTransferItemToOtherShop (Item item)
     {
         if (this.gold >= item.price) {
             gold -= item.price;
             AddItem (item, otherShop);
             RemoveItem (item, this);
             RefreshDisplay ();
             otherShop.RefreshDisplay ();
         }
 
         if (otherShop2 != null){
 
             if (shop2 == 1) {
                 AddItem (otherShop2.itemList [0], this);
                 AddItem (item, otherShop2);
                 PlayerPrefs.SetString ("cesto", item.itemName);
                 otherShop2.itemList.RemoveAt (0);
                 RemoveItem (item, this);
                 shop2 = 0;
                 backbutton.onClick.Invoke();
                 RefreshDisplay ();
                 otherShop2.RefreshDisplay ();
             }
         }
 
         if (otherShop3 != null){
 
             if (shop3 == 1) {
                 AddItem (otherShop3.itemList [0], this);
                 AddItem (item, otherShop3);
                 otherShop3.itemList.RemoveAt (0);
                 RemoveItem (item, this);
                 shop3 = 0;
                 backbutton.onClick.Invoke();
                 RefreshDisplay ();
                 otherShop3.RefreshDisplay ();
             }
         }
 
         if (otherShop4 != null){
 
             if (shop4 == 1) {
                 AddItem (otherShop4.itemList [0], this);
                 AddItem (item, otherShop4);
                 otherShop4.itemList.RemoveAt (0);
                 RemoveItem (item, this);
                 shop4 = 0;
                 backbutton.onClick.Invoke();
                 RefreshDisplay ();
                 otherShop4.RefreshDisplay ();
             }
         }
 
     }
 
     private void AddItem(Item itemToAdd, ShopScrollList shopList)
     {
         shopList.itemList.Add (itemToAdd);
         FileStream fs = new FileStream ("save.dat", FileMode.Create);
         BinaryFormatter bf = new BinaryFormatter ();
         bf.Serialize (fs, itemList);
         fs.Close ();
     }
 
     private void RemoveItem(Item itemToRemove, ShopScrollList shopList)
     {
         for (int i = shopList.itemList.Count - 1; i >= 0; i--) {
             if (shopList.itemList [i] == itemToRemove) {
                 shopList.itemList.RemoveAt (i);
             }
         }
 
         FileStream fs = new FileStream ("save.dat", FileMode.Create);
         BinaryFormatter bf = new BinaryFormatter ();
         bf.Serialize (fs, itemList);
         fs.Close ();
     }
 }