repeating FON

Hi hope someone can help I've tried the usual googling around and can't really find any answers,

Dose anyone know if you can repeat a BT fon/wifi with a wifi repeater now I'm guessing obviously you can connect to it with the repeater but would the login page still be forwarded etc,
My cousin can pick up a BT fon at her house but only with her laptop if she sits next to the window, She hardly ever uses the laptop and is more prone to using phones/tablets which don't have as strong a wifi card as her laptop so even in the same spot the signal is on/off all the time,
So would i be able to use a wireless repeater in said window as I'm guessing the repeater would have a stronger antenna in and repeat the signal for her while still passing the login page on. she can use my wifi details so it will be free for her she's not a heavy user so don't see the point in the expense of a phone line ETC or even mobile broadband if we can get this working for her

Thanks for advice Ash

I think it should work, sign in pages for WiFi have worked like this hotels when I've used a dongle to create Ethernet i.e. dongle in the one place you can get the signal then Ethernet to the desk.

thanks for the reply will give it a go next time I'm over at hers as see how we get on, see if i can dig my old drink router with DDWRT firmware on and use the repeater function on that

Ash