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Actually I have this app called FileExplorer pro installed on my phone. I used that to backup my pics to my NAS drive and it was able to copy the live photos painlessly. Apparently it turns out that each live picture has 2 components to it; a jpeg file and a QT file ( for example a live pic IMG_001 will have two files associates with it, eg IMG_001.JPG and IMG_001.QT ) So photostream and other programs end up copying just the JPG file and not the QT file which is why we end up only seeing the still version of the live pic. It is sad that Apple has not included an easy way to backup live pics but so far I have found FileExplorer to be the most painless way of transferring pics. I am sure Google Photos works well but it still does not solve the problem of being able to transfer pics directly from the phone to your local machine.
 
ok, so I backup my photos to Dropbox, which is supposed to be the full file, but my Live Photos are only showing up as regular photos. I even tried downloading those photos to my 6S and they lose their "liveliness". Anyway to back them up?

Tried google photos too, and they become regular photos there too.

Google Photos can backup live photos. They actually play them back looped if viewed on the google photos app on iOS.
 
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