Use parent description for variation.

description.php

<?php

/**
 * Use parent's description.
 */
function iconic_woocommerce_short_description( $description ) {
	if ( ! is_archive() ) {
		return $description;
	}
	
	global $product;
	
	$parent_id = $product->get_parent_id();
	
	if ( $parent_id <= 0 ) {
		return $description;
	}
	
    return get_the_excerpt( $parent_id ); 
}; 
         
add_filter( 'woocommerce_short_description', 'iconic_woocommerce_short_description', 10, 1 );