Praise be to Allah.
If your using the internet will not lead to increased charges for this person because of your downloading or uploading anything via the internet, and will not cause any slowdown or other problems because of increased traffic or sharing the connections, then the general meaning of tolerance between neighbours and the hadeeth of Abu Hurayrah in which the Prophet (peace and blessings of Allaah be upon him) said “No neighbour should prevent his neighbour from fixing a piece of wood to his wall” (narrated by al-Bukhaari (2463) and Muslim (1609)) indicates that it is permissible for you to use the internet in this case, but in order to be on the safe side it is better to ask your neighbour’s permission if you know him.
But there are some reservations concerning this issue, such as if the area is covered by more than one connection belonging to more than one neighbour, so your computer may connect to one at one time and another at another time.
There is also the issue of the losses of customers and profits incurred by the telecommunications company because of this taking advantage of neighbours’ coverage. Hence to be on the safe side it is better to sign up for your own account so that you may avoid these dubious matters.
And Allaah knows best.
Shaykh ‘Abd al-Rahmaan al-Barraak