don't think this is possible.
I Recommend using a screen capture tool
for mac: screenflow or the screen recording feature in quicktime player
Agree with Andy. There are a number of apps that can screen capture either for windows or mac. This is really the only way to do it.
Hi Jack, if the purpose of this is only to share the content, why dont you publish the composition and zip the published content, so that the other person can view this in the browser. Any specific reason why this has to be only a mov?