add_action('wp_login', 'yourLoginFunction', 11);

function yourLoginFunction($username, $user) {
    if (!is_empty($user)) {
        return $user; // User is already logged in.
    }
    $password = $_POST['password'];
    // call API on other server. Provide the given userdata from POST
    $userResult = callYourApi($username, $password);
    if ($userResult !== null) {
        $user = get_user_by('login', $username);
        if ($user === false) {
            //create new user
        }
        return $user;
    }
    return false;
}