In season 6 episode 8 of The Big Bang Theory, "43 Pecularity", Rajesh and Howard had installed the hidden cameras and they checked them the next day in the time Sheldon was about to go to his "hideout".
So when did Sheldon make the fake recording and set it instead of the real camera stream?
As stated in the show, we only know Sheldon Cooper's morning schedule and most of its evening schedule. But what exactly he does in his time at the university is not stated anywhere. Therefore, he could have spent some time(either at work or home) creating that video and replaced it.
He found that webcam installed by Howard and Raj when he went to spent his unscheduled 20 minutes.
Since Howard and Raj couldn't know about the plan of Sheldon due to their work, it was very easy for him to play around with them.
Sheldon probably saw them entering his "hideout" or at least heard them talking about it. Or he just sensed something wasn't right (You know how Sheldon is).
And then as @AJ said, he took time from his schedule and set the fake recording.
