I have both a Samsung Galaxy Tab 10.1 and also a Tab S 10.5. With both I use "ALLRELI" OTG cable to connect to a memory stick and COPIED data back and forth. I Purchased the "ALLRELI" from Amazon. Works well.
Then when you are in a more Wi-Fi accessible area you can use the sync.
Why have you set it up to sync, rather than save?