The simple reason is you are not buying the item from the original store, but from my USA partner. My partners buy the goods from the store in their own name so they need to keep the original tax invoice for their own tax records. This is exactly the same as if you bought an item from a store here in Australia - they will provide you with an invoice from them, but they will not provide you with a copy of their invoice from their wholesaler (i.e. who they bought the item from).
Normally a copy of the store invoice will be of no use to you since it is both from the USA and not in your name. It will almost certainly not allow you to make a warranty claim here in Australia. Your invoice are the invoices my USA partners supplies you when your items are shipped since that is who you have bought the item(s) from.
If you need to make a warranty claim on an item then please get in contact with me and I will advise you on what to do. In most cases we can help you make a US warranty claim (some warranties can't be claimed because it is not possible to ship the item back to the USA if it is defective).