What you are trying is not possible. Server B has no knowledge of the Client, so there is no way it can communicate with it. You should build it like this:
Client --> Server A
Server A --> POST --> Server B
Server A <-- REPLY <-- Server B
Client <-- Server A
In (pseudo)code, on Server A:
function handleRequest($postdata) {
$reply = sendPostToServerB($secrets);
return $reply;
}
$r = handleRequest($_POST);
$stufftosendtoclient = process($r);
echo $stufftosendtoclient;
When you do this, be wary of timing problems. If Server B is slow, it might cause issues in the client. You could try to handle this in an Ajax call and give the user at least more info and control of what is going on.