While we can't change your App Store subscription, or that of a gift recipient, we can switch you over easily to a Web-based subscription that also provides full access through our iOS app. When the campaign is over, you or your gift recipient will be asked if you have an existing subscription and, if so, if it's through the App Store.
If it is, we'll ask you to send us a screen capture (press the power standby button, and, while holding it, press the Home button) of your current subscription after switching the Auto Renew setting to Off. We can then use that information to add a year to whenever your current App Store subscription expires.
You or your giftee doesn't lose any unused portion of the App Store subscription. After the App Store subscription expires, you'll need to activate the Web subscription in iOS, which involves tapping a button in the app to send an email. It's very simple.