Yes, your shopper can save their designs in your store after customizing the product. Here is how your customer can do it.
Initially, your client needs to make an account in your store.
Once the account is created, your shoppers can save the designs on your store. After the user is done with designing the product, they can save it by pressing the “Save Design” button.
After entering the Design Title and saving it, your user can see the saved designs in the My Designs tabs.