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 or your photo in the upper-right hand corner
Click on Purchased > Not on this iPhone.
Find Business Card Reader Pro application in the list.
Tap the Download icon.
More information could be found in the following article of Apple Knowledge Base.