woocommerce-persistant-checkout-3.php

<?php

add_action( 'woocommerce_ship_to_different_address_checked', 'get_persitent_ship_to_different' );

function get_persitent_ship_to_different ( $value ) 
{
    $data = WC()->session->get('form_data');
    if ( ! $data || empty($data['ship_to_different_address']) )
        return $value;
        
    return is_bool($data['ship_to_different_address']) ? (int) $data['ship_to_different_address'] : $data['ship_to_different_address'];
}