I do not know how (or what meta) you used to store that value, So i cannot give you full code.
You can use following code in your theme’s (child theme’s if you are using) functions.php (change necessary code to get that link from user profile)

add_filter( 'fep_eb_email_legends', function( $legends, $mgs, $user_email ){
    $link = '';
    if( $user_email && ($user = get_user_by( 'email', $user_email ) ) ){
        $link = 'Here get that link from $user profile';
    }
    $legends['one_click_login'] = array(
        'description' => __('One click Login link', 'front-end-pm'),
        'where' => array( 'newmessage', 'reply' ), //where this tag will be used
        'replace_with' => $link
    );
    return $legends;
}, 10, 3);