You can share Live Photos on Facebook but only iOS devices on iOS 9 or later will see the animated version, everyone else will see a still image.
Here's how to share to Facebook:
- Open the Facebook app on your iPhone
- Select a Live Photo (you can see that it's a Live Photo as it will have a Bullseye icon on it).
- Tap Done
- Scroll down on the photo so you can see the Live icon at the bottom left and tap it to turn on Live. If you don't do this it will only post a still photo
- Tap Post
- When you view the photos in Facebook, just press and hold on them to view the moving image
You can only share Live Photos this way, if you try and share from the Photos app using the Share Icon you won't get the option to share the Live Photo, just a still.
It's also annoying that when you view the albums in Facebook you won't see the Live Photos album, even though it's there when you view your Photos app.
We suggest you find the Live images you want to share and put them in an album to make finding them when you are in Facebook easier.
We have tips for taking better Live Photos here: How to take Live Photos on iPhone
We also have a tutorial on How to Add Live Photos to Instagram.