Question

How to get access to ABBYY Account in BCR application, if you no longer have access to the original email account linked to it?

Answer

You can sign in to your ABBYY Account in BCR with your previous email account even without having access to it. In the app go to the Settings > tap ABBYY Account > Sign in > enter the email and password. After you signed in, wait till the cards are synchronized in the application.

Then you can sign out and create a new ABBYY Account with your new email as it is described in the article:
How to create an ABBYY Account in BCR for iOS
How to create an ABBYY Account in BCR for Android

Additional information 

How do I synchronize my business cards in Business Card Reader application?