In woocommerce, is it possible to make payment of one customer order by another customer?

It is indeed possible.

An order could be generated either via customer A or via the orders screen on the backend.

I’m unaware of a way to get the URL to pay from any admin screens as an existing feature but there is a function to get the payment URL.

You would basically pass in the order ID of customer A and it will show the URL to give to customer B. Use the following snippet where $order_id is the order number of customer A:

$order = wc_get_order($order_id);
$pay_url = esc_url( $order->get_checkout_payment_url() );
echo $pay_url;