How to copy and paste After Effects layers, clips to another file?

Hey, this is a question as old as time. Or I am just stupid. 

But shouldn't it be possible to copy a clip (let's say an edited jpg. with motion) to another After Effects file? Something like Essential Graphics for Premiere.

All I ever get is, that the footage is missing. And even when I replace the footage, the motion, transformations, effects etc. are gone.

Please can someone understand what I mean and help me.