This is the official Autel answer:
Hello,
Unfortunately, we do not have a way to back up missions. The only way to save mission data would be to create the mission on a third party software system, such as Google Earth Pro desktop, then save a copy of the mission to your desktop and then import the created mission into the explorer app via a KML file.
It still wouldn't save to the explorer app on the new device, but you would have a copy of the mission that can be reimported to the explorer app on an alternative device via a KML file. I've included a step by step guide in the attachment section on how to create, save, and export a KML file into the explorer app if you would like this information for future use.