Popcorn Time and IP changes

So,
If been two weeks by family of mine in the vacation around the Christmas days.

Now after 2 too 3 weeks they have received a letter from the lawyer that someone downloaded a film on their WiFi ip. I have watched the film mentioned in the letter on popcorn time, so I’m wondering if that’s illegal in Germany. In the letter was also mentioned that I have spread the film across the Internet. Further on they mentioned a IP address in the letter of the used device that does not match the ip address of my laptop if I look at whatsmyipadress.com, so my question about that is: Does my IP of my computer change if I log on too another WiFi router?

I really hope you can help me, cause the payment is about €2600,- and I’m literally just 15… I’m not hoping to pay this.