The speed with which Lindy acquires a luxury apartment, and the ease with which she enrolls Fate in Nanoha's school, implies that the TSAB has influential behind-the-scene contacts on Earth. Since Admiral Graham hails from the planet, and is in fact Hayate's financial supporter and presumably legal guardian, this seems quite plausible. Magical Girl Lyrical Nanoha StrikerS makes this a bit more explicit in its first Sound Stage, where Suzuka and Alisa — both members of wealthy and influential families — have become TSAB civilian consultants whose job it is to help with matters like this.
