Yes. If you would like a copy of the store invoice, just include "please send me copy of store invoice" in the extra details box. Because of the extra work involved for my US partner there is a US$5.00 fee for this service if requested at the time of placing the order.
The fee for obtaining a copy of the store invoice made after the order is shipped is US$15 unless your item is broken and you need the store invoice to make a warranty claim here in Australia. If you need the store invoice to make a local warranty claim here then this fee will be waived, but you must determine that an USA invoice in another person's name will allow you to have a item repaired in Australia (or your country) since in most cases it will not.