Yes!
You can update your shipping address within 6 hours after the order is placed or until the order ships (whichever comes first)
Here's the process:
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Log into your account here: https://account.rainierwatch.com/
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Then click on the order that you want to change
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Under "Edit Your Order", click "Shipping Address" and add the new shipping address!
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Don't forget to hit "save address"