The APIs have been made to allow programs to communicate without the old problems like this one. Chevereto comes with an end-point (api.php) that you can trigger to perform upload operations from almost anything out there. If you want that Chevereto hooks things that belongs to phpbb (like add user sessions and things like that) you will need more work than just call the API.
I believe that the best for you is create a bridge or connector. A bridge is a way to have something in the middle that makes the communication between the systems. In Chevereto.com I have a connector to xenforo and when the forum was punbb I also had a custom punbb connector. The key is load it at an early line in the Chevereto code execution. When you load phpbb it will declarate its variables and classes. You only need to copy them to new variables, like $phpbb_user = $user; That will create a copy of $user and you can access using $phpbb_user. Later in the PHP execution Chevereto will overwrite this original phpbb $user with its own $user and everything will work. Since you changed the default phpbb $user, you will need to call it always as $phpbb_user from now on (Chevereto code).
Notice that if phpbb and chevereto share functions like I don't know... get_config() or things like that, Chevereto will also override those. Take note that the best practice is use this connectors to get and set data. Not to extend functions of phpbb inside Chevereto and you shouldn't rely in the phpbb functions when doing this. In that case you can easily create functions like is_phpbb_user() in the very same connector and call that function inside Chevereto, maybe clone the phpbb needed functions or objects. Try to don't call direct phpbb functions.
