I filed a copyright form TX if I remember right back in 2001 for my software and Philip Frankel (my copyright lawyer) said that I only needed the first 50 lines of code and the last 50 lines. I told him, software isn't linear anymore.
Anybody can file a copyright claim, but when you do, the government doesn't check for the validity of that claim. They just require a signed oath that you're not filing a false claim (which is punishable). So long as the real Satoshi doesn't contest this claim, Craig Wright is safe.
Obviously, the real Satoshi wants to remain anonymous or is dead.