How to add sub menu item under specific menu?

Hello, I’m trying to add login/logout menu items as sub-items under specific menu (menu name is : author-menu)
My top menu item’s id is written as menu-item-7618 but I’m not sure how to write it I tried both but did not work.
Would you please check the code below?
It does not throw any error but does not do anything either.

function add_menu_parent_class( $items ) {

		if( is_admin() ||  $args->theme_location != 'author-menu' )
		return $items;

		$redirect = ( is_home() ) ? false : get_permalink();

		if (is_user_logged_in() &&  $args->theme_location != 'author-menu')
		{

			$userdata =  wp_get_current_user();
			$link = '<a href="/sign-in" title="' .  __( 'Login' ) .'">' . __( 'Login' ) . '</a>';

			$link_profile = array (
				'title'            => 'Logout',
				'menu_item_parent' => 7618,
				'ID'               => '234234234234234',
				'db_id'            => '234234234234234',
				'url'              => $link,
			);

			$items[] = (object) $link_profile;
		}
		else
		{
				$link = '<a href="' . wp_logout_url( $redirect ) . '" title="' .  __( 'Logout' ) .'">' . __( 'Logout' ) . '</a>';

				$link_logout = array (

				'title'            => 'Login',
				'menu_item_parent' => 7618,
				'ID'               => '5746734534',
				'db_id'            => '5746734534',
				'url'              => $link,
			);
			$items[] = (object) $link_logout;
		}
	return $items;
}
add_filter( 'wp_nav_menu_objects', 'add_menu_parent_class',50,2 );