Payment information is account dependent. You can re-install the Pro version you have previously bought without paying for it again if you simply make sure you do so from the same user account you purchased it from.
Open the Play Store app on your Android device. Check that you are connected with the same account that you used to make the purchase from. Open the hamburger menu (the three stacked lines at the top left of your screen) and tap “My apps & games”. Tap on “Library” and then look for the “Shopping list voice input PRO” app and tap on the “Install” button next to it.