Most residential lines are DHCP not static so a history search will probably just waste your time. If you truly have their IP then you have a good legal foot to stand on.
I have already been working with multiple authorities. The second avenue I am pursuing is a civil case.
It is a dynamic IP so it is possible the node was not run by the hacker and it just so happen the hacker got an IP of a guy who did run one from mid December through mid January but that is fairly unlikely. From my understanding generally ISPs will not cycle an IP very often and if they do it won't happen unless you reset your router which people don't do very often.