The media library on LDS.org has a section of Social Media Shareable Videos.
This is a collection of short videos that have been published on Church social media pages.
This is a great library of videos you can share with others on social media. Below are a few of my favorites:
Strong Family, Strong Nation
Blessed with Great Joy
Challenges Strengthen Us
He Understands
Find many more shareable videos like this in the LDS.org media library section of Social Media Shareable Videos.
