If your client registered by choice without reaching the compulsory registration threshold of $75,000 then the answer is no. He gets to keep the money. He is only required to report the GST on the invoices issued after 1 July.
However, if your client reached the threshold and was required to register then he must forfeit 10% as GST payable to the ATO. He could reissue the invoices adding the 10% GST onto the original cost, but the customer is obliged to pay only on the original invoice issued—so good luck getting the extra money from the customer!
Because he is on cash reporting, for the purchases, he should claim the GST credits as he has paid for the goods in July.
Edited at 19 Jan 2017 06:38 AM GMT