You could acquire this by simply adding edit.php link to the admin_url() in jonnyplow‘s code.
add_action( 'register' , 'register_replacement' );
function register_replacement( $link ){
if ( ! is_user_logged_in() ) {
if ( get_option('users_can_register') )
$link = $before . '<a href="' . site_url('wp-login.php?action=register', 'login') . '">' . __('Register') . '</a>' . $after;
else
$link = '';
} else {
$link = $before . '<a href="' . admin_url() . 'edit.php">' . __('Your Title Here') . '</a>' . $after;
}
return $link;
}