add_filter( 'woogc/ps/synchronize_product/child_product', 'sync_custom_taxonomy_to_child_product', 10, 3 );
    function sync_custom_taxonomy_to_child_product( $child_product, $main_product_data, $origin_product_blog_ID )
        {
            $taxnomy_name   =   'writer';

            //switch back to the origin product shop
            switch_to_blog( $origin_product_blog_ID );

            $main_product   =   new WC_Product( $main_product_data[ 'id' ] );

            $main_product_terms_ids =   wp_get_object_terms( $main_product->get_ID(), $taxnomy_name, array( 'fields' => 'ids' ) ) ;

            restore_current_blog();

            if ( count (  $main_product_terms_ids ) > 0 )
                {
                    $WooGC_PS   =   new WooGC_PS();

                    var_dump( $main_product_terms_ids );
                    var_dump( $child_product );
                    var_dump( $origin_product_blog_ID );
                    var_dump( $taxnomy_name );

                    //$WooGC_PS->synchronize_taxonomy ( $main_product_terms_ids, $child_product->get_ID(), $origin_product_blog_ID, $taxnomy_name );
                }

            return $child_product;
        }