Greg Egan's Permutation City!
Sort of, at least it involves uploading consciousness, not so much with the internet though. I adored it, but I read it about 25 years ago and you have to remember that the internet was still in 'cardboard, paint and sticky tape' phase then, so I don't know how it will hold up today.
"Total Recall," especially the first one with Arnold Schwarzenegger, did a very good job with this idea.For some reason this is a subject that seems to attract action movies a lot. Are mind swap (using technology) movies of interest to your search?
I just finished watching Self/Less - an action movie with Ryan Reynolds. It was enjoyable enough.
The Anomaly - another action movie with Noel Clarke and Ian Somerhalder. The acting could be strained in places, the story was pretty good. Some decent fight scenes.