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:
Make sure you sign in with Apple ID that you used for the original purchase.
Launch App Store on your mobile device.
- Tap the account icon ( or your photo) in the upper-right corner.
Click Purchased > Not on this iPhone/iPad.
Find the ABBYY application in the list.
Tap the Download icon.
More information could be found in the following article of Apple Knowledge Base.