Cinemagraphs can be copied to a PC and back to a mobile device by connecting the device and the computer with a USB cable. Be sure to copy both the .npo and the .gif files associated with a cinemagraph. For Apple computers, download and use Windows Phone Connector Software for this.
You cannot backup cinemagraphs for SkyDrive as it does not support the cinemagraph format. It is possible to upload cinemagraphs in gif format to SkyDrive, but they can’t be downloaded back for further editing.