To get the Facebook Third Party ID for your app Facebook user, try the following code using Graph API:
$fbid = $facebook->api('/me?fields=third_party_id&access_token='.$access_token);
echo "THIRD PARTY ID: ".$fbid['third_party_id'];
What is Third Party ID?
Facebook expressly prohibit Platform developers from passing any data from Facebook to data brokers. But sometimes there are practical reasons that developers will need to share information with a legitimate third party and so there comes 3rd party ID.
For instance, a game developer might need a way to identify that a user has taken an action on a partner website (e.g., completed an offer) so that the person can receive virtual goods. For this reason, we have developed a mechanism for developers to obtain an anonymous but unique identifier for their users, which we call a third-party identifier.