An interesting aspects of sharing to Facebook from your app is that when people engage with the news feed stories posted from your app. Those stories can send people to your app or your app's App Store page which drives traffic and app installs. You can implement this behavior using App Links.
When you set up App Links, you can control what happens when someone taps on one of the links shared through your app or on the story attribution (name of your app) in one of the Open Graph stories shared through your app. If your app has web content, people see a web view of that content.
If your app is installed there may be an Open button that launches your iOS app. If your app isn't installed, people see aninstall option to directing them to your app's App Store page. If your app is mobile-only and has no web content, when someone clicks the shared link they either open your app if it's installed or go to your app's App Store page (if your app isn't installed. The image below shows this flow: