The image is not stored at any point. The receiver and the transmitter are part of the same electric circuit in a certain sense. It's a virtual circuit but the entire thing - transmitter and receiving unit alike - are oscillating in unison driven by a single clock.
The image is never entirely realized as a complete thing, either. While slow phosphor tubes do display a static image, most CRT systems used extremely fast phosphors; they release the majority of the light within a millisecond of the beam hitting them. If you take a really fast exposure of a CRT display (say 1/100,000th of a second) you don't see the whole image on the photograph - only the most recently few drawn lines glow. The image as a whole never exists at the same time. It exists only in the persistence of vision.