If you need to control the image that is used when shared to facebook, might I suggest doing the following within Yoast SEO:
- Once the plugin is installed, you will have a Yoast SEO settings panel below your post and page editor.
- On this panel there is a social tab. Within this tab you are given the ability to edit the image used when users share via Facebook and Twitter.
As an added bonus, you can control the title and description as well.
*EDIT 4-24
I have a portfolio site that uses animated gifs as featured images and I had to use the plugin Animated GIF Resize
Sometimes there is not a simple function that can be added unfortunately.
*EDIT - Tested and works when sharing link to posts with featured image from gif to Facebook.