The App Store will not let you purchase the same unlock twice (there are only two unlocks: one for iPad and one for iPhone/iPod touch). So you can always purchase it again.
However, the "Restore Purchases" button is the normal way to handle this if you have already purchased the unlock elsewhere:
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Download MIDI Designer Lite from the App Store
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Tap on the Lite icon on the Lite Bar
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The "restore purchases" button appears on the bottom left. Log in to the App Store and your Pro unlock will be active.

Comment here or get in touch via Config -> Actions -> Email Us if you encounter any issues.
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