Change Woocommerce checkout to process order on an separate WordPress site?

Try this way

Add this code in site A.

function action_woocommerce_new_order( $order_id ) { 

    //get all order details by $order_id    
    //post your data to site B

    $ch = curl_init();

    curl_setopt($ch, CURLOPT_URL,"http://yoursiteB.com/wp-json/api/v2/create_wc_order");
    curl_setopt($ch, CURLOPT_POST, 1);
    curl_setopt($ch, CURLOPT_POSTFIELDS,
            "postvar1=value1&postvar2=value2");

    // In real life you should use something like:
    // curl_setopt($ch, CURLOPT_POSTFIELDS, 
    //          http_build_query(array('postvar1' => 'value1')));

    // Receive server response ...
    curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);

    $server_output = curl_exec($ch);

    curl_close ($ch);
}; 
add_action( 'woocommerce_payment_complete', 'action_woocommerce_new_order', 10, 1 );

Add this code in site B.

Class WC_Rest_API {

    public function __construct() {
        add_action( 'rest_api_init', array( $this, 'init_rest_api') );
    }

    public function init_rest_api() {
        register_rest_route('api/v2', '/create_wc_order', array(
           'methods' => 'POST',
           'callback' => array($this,'create_wc_order'),
        ));
   }

    public function create_wc_order( $data ) {

            //$data  - all the details needs to be send from site A

            global $woocommerce;
            $user_id = $data['user_id'];
            $user = get_user_by( 'ID', $user_id);
            $phonenumer = get_user_meta( $user_id,'user_phoneno', true);

            if($user) {         

                $address = array(
                  'first_name' => $user->display_name,
                  'last_name'  => $user->display_name,
                  'email'      => $user->user_email,
                  'phone'      => $phonenumer,            
                );

                $order = wc_create_order();
                //get product details from rest api site A
                $order->add_product(); 
                $order->set_address( $address, 'billing' );

                $order->calculate_totals();         
                $order = wc_get_order( $order->id );

                $response['status'] = 'success';
                $response['message'] = 'Order created on wordpress site B.';    
                return new WP_REST_Response($response, 200);

          }

    }       
}

$rest_api = new WC_Rest_API();

Send all the data from site A to site B via below the URL.

http://yoursiteB.com/wp-json/api/v2/create_wc_order

Method should be 'POST'

Data should be contain all the details od order from site A.

Let me know if you have any question.