Link categories to last post

This could be done with a ne walker class

class Childcat2LastPost extends Walker_Category
{
    function start_el( &$output, $category, $depth = 0, $args = array(), $id = 0 ) {

        if ( 0 != $category->category_parent ) {

            $args = array(
                    'cat'            => $category->term_id,
                    'orderby'        => 'post_date',
                    'order'          => 'DESC',
                    'post_type'      => 'post',
                    'post_status'    => 'publish',
                    'post__not_in'   => get_option( 'sticky_posts' ), // do not display sticky posts
            );

            $query        = new WP_Query( $args );
            $recent_posts = $query->get_posts();
            $last         = sizeof( $recent_posts ) -1;
            $last_post    = $recent_posts[$last];
            $permlink     = get_permalink( $last_post->ID );
            $title        = $last_post->post_title;

            if ( ! empty( $permlink ) ) {
                $output .= sprintf( '<li><a href="https://wordpress.stackexchange.com/questions/97531/%s">%s</a></li>', esc_attr( $permlink ), esc_html( $title ) );
            }

        } else {

            parent::start_el( $output, $category, $depth, $args, $id );

        }

    }
}

You have to pass the class as argument to wp_list_categories

$cat2post = new Childcat2LastPost();

$args = array(
    'walker' => $cat2post
);

echo '<ol>';
wp_list_categories( $args );
echo '</ol>';

Comment out the line 'post__not_in' if you want to include sticky posts. Adjust the HTML in the line with $output .= sprintf( '<li><a href="https://wordpress.stackexchange.com/questions/97531/%s">%s</a></li>', esc_attr( $permlink ), esc_html( $title ) ); (add an alt and/or title attribute, a class etc).

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