Facebook share is the easiest to implement, and most widely used Facebook marketing tactic for advertisers to use on their own website. With Facebook share, you can easily format news, articles, audio, and video to be seen on Facebook when a user elects to post your content to their news feed; the result, an automatic endorsement from one Facebook user, to all of their friends.
But Facebook caches already shared urls/pages for better performance. This causes issues at time when we update the title, picture being shared or the description of the page because facebook still shows the older version of the page.
Facebook has a developer tool called Debugger. This tool gives us an idea about how a url will be shared on facebook, what content, which image will be fetched. You can use this tool for any url and it fetches the latest title, description, excerpt and other stuff that will be shown while sharing the link. If you use an already shared URL with this tool then facebook fetches the latest content, and also updates it cache with the latest content.

Screenshot: Facebook Debugger: Clear Facebook Share Caches
With this methos the url remains the same hence the share count will persist and the content will be updated. Someone else sharing the url will also see the latest content now.
More details about Facebook Share, click here: How to share links and other content.