Dynamic render texture within prefab's camera?

Hi guys!

For a school project I want to create a room full of screens, showing footage of camera's that are following your game character. Through render textures this is possible, but if I create a prefab from my set-up (one plane showing the texture and one camera to get the footage), it keeps showing footage from the point of view of the initial camera whenever I place a new prefab somewhere.

Is there some way (probably through scripting) to get a render texture from the camera of each new placed prefab?

Thanks a lot in advance!

Best, GierigBeefje