Yes, you certainly can!
Use either a King profile or Facebook to easily switch between devices and access your game progress and Gold Bars wherever you play. Boosters and extra lives however, are always stored locally on the device you received them on, so they won't move across devices.
There is a King profile option in your settings menu. Look out for the orange King button and you can keep your social media separate from your gaming, but still benefit from thousands of other King players who can send you lives.
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