Since the very first version of MealPlan, my goal all along has been to enable syncing your grocery list to your iPhone. iCloud was the obvious way to do this, and MealPlan is designed from the start with iCloud sync in mind.
iCloud makes it really easy to sync data between devices you own. Apple takes care of the synchronization, and there are no separate accounts or logins to manage. It's all done within the iCloud umbrella.
MealPlan now supports creating Reminders from your MealPlan grocery list. Tap the Action button at the bottom of the grocery list, choose to Send to Reminders, and a new list will be created in the Reminders app that contains your grocery list.
And because iCloud supports sharing reminders with other users, you can share your grocery list between your iPad and iPhone devices and your Mac, even if they don't all share the same iCloud account. (For details on how to do this, see the MealPlan FAQ).
This works very well, and is supported in MealPlan 1.4, available now in the App Store.