If you want to use the phpBB WordPress integration plugin just to transfer users between WordPress and phpBB or phpBB to WordPress, follow instructions on this help page:
How are users identified when you add/transfer existent user
integration of same username/email users
Problem: i have WordPress users and I have phpbb users, they have different usernames but the same email addresses.
user A into phpBB with email C
user B into WP with email C
user A into phpBB come to try to login WP: NOT added can’t login WP side.
If you use the transfer process of WP users into phpBB:
user A Same above.
user B transferred into phpBB, B now can login into both phpBB and WP.
You’ll have two users into phpBB with same email, which is possible as option into phpBB.
You can also merge posts/users into one user in this way:
Change email to the user B in WP.
Login with the phpBB user A into WP, that will be added, as no same email found.
Now delete user B in WP, and retain posts assigning to A.
Result: an unique user, with all his posts on both phpBB and WP.
NOTE: This is just to give an idea on how to resolve common problems about an integration with pre existent users in phpBB that may have same email. But there are several more possibilities: in phpBB ACP there are many options to manage users and posts, and combining these and from the above, you should get the way to resolve any possible scenario.
Based on this topic: How are users identified? (when adding/transfer existent users)