All applications, including ABBYY applications, which you purchase in App Store are associated with your Apple ID.

To install the purchased application again, please do the following:

1. Make sure you sign in with Apple ID that you used for the original purchase.
2. Launch App Store on your mobile device.
3. Tap the account icon ( or your photo) in the upper-right corner.
4. Click Purchased > Not on this iPhone/iPad.
5. Find the ABBYY application in the list.
6. Tap the Download icon.

More information could be found in the following article of Apple Knowledge Base.