If your store has an “Apply coupon” form somewhere allowing customers to enter their coupon code and redeem discount, then you can show list of their purchased GIFT4U gift card coupon codes under that form. They can select one from the list and apply it in an easier way.
Enable and customize this list with 3 options in General settings: (6) Show coupon list; (7) Coupon background color and (8) Coupon text color