• In the iphone app My Week, I don't believe there's a way to promote from the parking lot to a task, and it's impossible, I think, to move a task from one week to another.

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My Week (iPhone App)
Yes, you can promote tasks from the parking lot to the week by swiping left on it and then pressing the calendar icon.

In the next major update there will be an option for changing the date on tasks allowing for moving tasks between weeks. You can access the MyWeeks uservoice here:

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Hooray! I was just about to post a question about this because I couldn't work out how to move tasks either! Problem solve