I think what popatim was saying is to get a better external antenna for your device. He must have assumed you are talking laptop or desktop (though it does not look like you said what devices your grandmother uses). A couple of questions:
What wireless devices are in use in her apartment?
Do you know what direction the wireless signal is comming from?
What is your budget?
Also it would help if you would download a software like inSSIDer or an app like Wifi Analyzer. That would help in telling you the signal level of the wifi she is trying to get as well as any other wifi signals around. This is critical because if there is a wifi signal on the same channel that your apartment wifi is on, and that signal is stronger than the apartment wifi, then you could spend alot of money and still not have a workable connection.