Customer can send an old order again

Is it possible to send an old order again from historical ordering list?

Sure. Just change the order status and in the popup turn on the notification to the customer and that we send him an email with all the order information.

I worded the question poorly. I mean if the customer can press a buy button on an old order and get it in the cart again.

Therefore allow the customer to buy the same products again from an old order by one button press.

No, that's not possible. You can activate a "buy" button on the order listing of your customers so that they can pay orders which they didn't pay immediately. But you can't have them load all the products from a previous order in the cart. That would require some custom coding.