Can Aperture convert .mov files for iPhone use?

I use Aperture to organize and edit all our family photos and videos. In iTunes, we synchronize portions of our Aperture library to a family of iOS devices. I notice that the videos I shoot with our Sony RX100-2 camera upload fine to Aperture, but generate an error when attempting to sync to our iPhones (4, 4S, and 6). These videos are in .mov format.

Is there some convenient way to solve this so that our videos will all work with our iOS devices? Any insights on how to address this situation, in Aperture, iTunes, or elsewhere will be appreciated.