Is one who helped his wife's sister install the internet, knowing that she would use it to download music, sinful, and is he obliged to remove what he installed?

You made a grave mistake by helping them install the internet, knowing it would be used for sinful purposes like music. Your duty was to forbid them and remind them of violating Allah's commands, not to assist them, for Allah Almighty says: ﴿And cooperate in righteousness and piety, but do not cooperate in sin and aggression﴾ (Al-Ma'idah: 2).

Your duty now is to repent, feel remorse, and resolve never to return to such an act. As part of your complete repentance, if you are able, you should proactively remove what you installed and rectify the mistake. If you cannot, then advise them to abandon sinful programs and limit themselves to what is permissible.