You'd be better off with a Powerline Access Point (e.g. click here extends the wired network from your router over your mains electric circuit and then creates a new WiFi Access point (with a different name to your existing WiFi) in the "remote" location. Much more reliable and higher speeds.
As much as range extenders can work, they slow the whole process down. In any event I could see extending an extender being fraught with problems. Not least because the router's WiFi and the existing extended WiFi (presumably) use the same name and a further one added (again if the same name) could be having difficulty deciding which (of the existing) to connect to and switching between them.