In the PHPBB directory, edit the file .htaccess and after RewriteRule ^(.*)$ app.php [QSA,L] you can enter:
RewriteCond %{HTTPS} off
# First rewrite to HTTPS:
# Don't put www. here. If it is already there it will be included, if not
# the subsequent rule will catch it.
RewriteRule .* https://%{HTTP_HOST}%{REQUEST_URI} [L,R=301]
# Now, rewrite any request to the wrong domain to use www.
RewriteCond %{HTTP_HOST} !^www\.
RewriteRule .* https://www.%{HTTP_HOST}%{REQUEST_URI} [L,R=301]