Not sure if this is the correct community for such a question, but I have been wondering for years how it is possible that e.g. people inside ISIS controlled territory continued to have internet access and such.
They use mostly satellite internet providers. Some of them are maintained by Iran, some are European. They are not used only by ISIS but also by Hezbollah and Al-Qaida. ISIS has very advanced equipment in terms of communication and internet connection.
Nowadays you can't just "shut down" internet in some area, it's widely distributed and the process of how the providing works don't make it simple to target ISIS individuals and shut them down from the internet. Also, the intelligence gained from this communication channels is beneficial for secret services.
I recommend reading this article, which very well explains the whole problem. https://www.wired.com/2016/03/how-is-isis-online/