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function sg_nav_description( $item_output, $item, $depth, $args ) {
    if ( 'primary' == $args->theme_location && $item->description ) {
        $item_output = str_replace( $args->link_after . '</a>', '<div class="sg-item-icon">' . $item->description . '</div>' . $args->link_after . '</a>', $item_output );
    }

    return $item_output;
}
add_filter( 'walker_nav_menu_start_el', 'sg_nav_description', 10, 4 );