Q: Shared Videos

You can use AirDrop to share the videos and then download them to your new iPhone.

Or you could get a Wireless Transfer App. Basically you install the app on both iPhones, connect them to the same Wi-Fi and then just transfer selected media to each other.

Learn more here: http://www.wirelesstransferapp.com/wireless-transfer-from-iphone-to-iphone.html# .V4j5yZOLTLZ

Good luck!

You can't transfer a shared video because it's not on your device in the first place. You have to save the video to the device first, if I'm not mistaken and you can only save a shared video to a computer. After you save the video, you can sync it back to the phone from the computer or use the Wireless Transfer app.

iCloud Photo Sharing - Apple Support

Anyone that can access a shared album can download the photos and keep them forever. On your iPhone, iPad, or iPod touch, tap the photo > > Save Image. On your Mac, select the photo or video, control-click > Import. You can only save shared videos to a Mac or PC.