All that AB's server sees is the IP address of the person submitting the post. Since most ISP's allocate IP addresses 'dynamically', all that anyone has to do to change their IP address is to log off and then log on again.
Additionally it's very easy to route traffic via an anonymous proxy server, so that the receiving website thinks the post is coming from somewhere other than its true origin. (Much of my internet posting is done through a set of proxies, which appear to show my ISP as being in Brazil, Slovakia or China, rather than here in the UK).
Only your ISP can link your IP address to your phone number (and to you). To pass on such information (even to official bodies, such as the police or security services) without a court order is a serious criminal offence, nearly always leading to imprisonment. So they definitely won't make such information available to sites like AB!
Chris