You may have to re-download the tables on another device, but as long as you're logged in under the same account on your devices the tables will be accessible. I frequently buy on my phone, and later play on my tablet.
Note however progress toward standard/wizard goals and local high scores will NOT carry over from phone to phone unless you move the saved data (which you can learn more about from other threads). Since I most often play on my tablet, every couple of weeks I send my save file to my phone, or vice versa.
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