You do not need a receipt, all you actually need is proof of purchase so your mother should check her bank statement for debit card purchases or check her card statement.
Cash purchases, of course ,are more difficult to trace. However, in the real world, I would be very surprised if the Store Manager failed to replace the item, purely as a good-will gesture.
If the item is not fit for purpose, it shouldn't really matter where the particular machine was bought from because the vendor will take up the issue with their supplier and this chain of events will be repeated back to the manufacturer, who, ultimately has produced an unsatisfactory product.