How to sync mobile site to desktop site

I have a WordPress blog for which I am setting up a mobile version with different installation of WordPress. But I realize that I can easily redirect my audience to the mobile site when a mobile device is detected, however I can’t seem to figure out how to automatically update the mobile site when I publish a post on the desktop site. My goal is sync the two version with same content and links but with a different theme.

I was wondering if any of you know of a way to solve my problem. Thanks in advance.