A previously posted service manual indicates the battery assembly for the PRS-600 is part number A-1732-035-A.
If you go to https://servicesales.sel.sony.com/ec.../web/index.jsp
and enter the part number in the search box and select "part number" in the drop down box, you will see if they are in stock and the price.
At the moment, they are not in stock and the price would be $76.15 plus shipping. (Ouch!)
The part numbers for the battery are indeed different for the PRS-505 and the PRS-600.