How To Add An Animation Into SFM?

So I am trying to create a scene in which my characters are watching a film in a cinema, I would like to know how I can maybe "project" an animation onto the screen (or something along the lines of replacing the large screen texture with an animated texture? I have no clue how to do that lol).

The animation itself is pretty short, like 3 or 4 seconds long and it's dimensions will be within the power of 2 so the source engine won't scream errors at me.

So can someone please help? thnx