unable to save select option when ajax reload on checkout

Hi, I couldn’t save selected option when ajax run in the checkout with my custom field. I saw it in Select and Textarea option

Reproduce>
go to checkout> fill the form> select payment method (this do the ajax by a plugin) > should re-select dropdown for this custom code above

add_action( 'woocommerce_after_checkout_billing_form', 'arca_checkout_field' );

function arca_checkout_field( $checkout ) {
	
    echo '<div id="arca_envio_checkout_field"><h2>' . __('Detalles de Envio') . '</h2>';
   
	woocommerce_form_field( 'arca_informacion_envio', array(
        'type'          => 'select',
        'class'         => array('select wc-enhanced-select form-row-wide'),
        'label'         => __('Método de Envío'),
        /*'placeholder'   => _x('Elige una opción..', 'placeholder', 'woocommerce'),*/
		'required'      => true, // or false
		//'clear'	=> false,
		//'default'     => '',
		'options'   => array(
		'' => __( 'Elige una opción..', 'woocommerce' ),
  		'pasare_retirar' => __( 'Pasaré a retirar', 'woocommerce' ),
		'enviar_por_delivery' 	=> __( 'Enviar por Delivery - Cobrado en la entrega el pedido', 'woocommerce' )),
        ), $checkout->get_value( 'arca_informacion_envio' ));

I tried to uso these code to save the selected option but didn’t work:

add_action( 'wp_footer', 'woocommerce_tip_script2' );
function woocommerce_tip_script2() {
    // Only on checkout page
    if( ! is_checkout() ) return;
    ?>
    <script type="text/javascript">
    jQuery(function($){
        // On 'select#arca_informacion_envio' change (live event)
        $('form.checkout').on( 'change', 'select#arca_informacion_envio', function(){
            // Set the select value in a variable
            var a = $(this).val();

            // Update checkout event
            $('body').trigger('update_checkout');
			//jQuery(document.body).trigger("update_checkout");

            // Restoring the chosen option value
            $('select#arca_informacion_envio').prop('selected', true);

            // Just for testing (To be removed)
            //console.log('trigger "update_checkout"');

            // Once checkout has been updated
            $('body').on('updated_checkout', function(){
                // Restoring the chosen option value
                $('select#arca_informacion_envio option[value='+a+']').prop('selected', true);

                // Just for testing (To be removed)
               // console.log('"updated_checkout" event, restore selected option value: '+a);
            });
        });
    })
    </script>
    <?php
}

It only happens with dropdown and textarea Options

any help? please

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