LiveToGIF lets you easily convert the Live Photos your iPhone takes into either animated GIFs or movies. This then lets you more seamlessly share them with friends and family.
Simply choose the photo youd like to convert and the app will process it and present you with the standard sharing sheet to let you easily share to Email, Messages, Facebook, etc.
You can also save the resulting files into your Photo Library for later use.
NOTE: To share on Twitter save the resulting GIF to your camera roll and then share using a Twitter client.