Is it possible to have the extender use the same SSID as the WiFi router, or must it be a different SSID name? If it uses the same SSID, your phone *should* roam when the signal gets weak to a better signal.
Another idea is to use a pair of powerline adapters to connect the extender to the original WiFi using ethernet (if running cable is impossible/prohibitive), which will have a faster signal to the extender and give better performance. Albeit at a co$t...