Awesome! I am deeply sorry for taking your time and thankful for your advice. I have skipped reading this manual. Actually I succesfully ignored the plugin’s header, where the info is linked (Install Steps, Help and FAQs | How To and Shortcodes list phpBB | WordPress Integration extension | ?? Support this Plugin). That big green button is too attracting there :).
Just maybe.. if possible.. may you add red warning “If your forum is on different domain or subdomain, read this!” or something? For future readers as dumb as I am. ??
Because of having forum od subdomain forum.* it is expected cookies can not work. All set now, all working.. thank you again. Cheers.