So i reset password of the alessio user to test directly there.
The reset password into phpBB have some issues but it seem to me the one in wp worked.
Then with my chrome tested the login in phpBB and the persistence, but as long i set the remember me option on login i see the cookies are correctly set: Then i navigate over some page not in phpBB and returning back i see the user alessio still logged in regularly. I actually cannot figure out the problem. I accessed to wordpress admin, and phpBB without problems.