Use of the trademark registration symbol (®) in the United States prior to securing a United States trademark registration is illegal. Last I checked the project was hosted on servers that physically reside in the United States. Despite your best efforts to remain in denial the fact remains the term "phpbb" is not a registered trademark in the United States. All you have done is apply to register the trademark and been denied on the first application. Do yourselves a favor and look it up yourselves, the USPTO is completely transparent and the database publicly accessible.
Following the steps below you can easily verify the current status of your trademark application:
That page is not the registration, it is merely the record of the application. You have to click on TARR status
where you will then notice the registration # and registration date are blank because there is no registration. The application was refused on the Principal Register for being merely descriptive of the product. Bottom line is that you do not yet have a registered trademark in the United States and to include the ® symbol prior to receiving a registration would be a violation of federal law.