You can use the same account on multiple devices. Simply make sure that the app is downloaded on that separate device, and log in using the same details that you have used on the original device.
If someone else is collecting your order a screen shot or message showing an order number will not allow you to collect the order. You will need to be logged into the account the order was placed under as there is still more to do when you arrive.
Until the order is paid for, the restaurant will have no record of it. Your order only exists on the account the order was placed under.