Yes, you can add your cards to the Apple Wallet application!
However, Apple Wallet currently only supports a few barcode types (QR, Aztec, PDF417 and Code 128 with iOS 9 or later). You can add all your rewards cards in Stocard with barcodes of these formats to the Apple Wallet application by opening the card menu (the three dots in the top right corner of your card screen) and then selecting "Add to Apple Wallet". Since Stocard supports more barcode types than the Wallet app, there might be cards in Stocard that you cannot add to the Apple Wallet though. We apologize for the inconvenience.