Yup! Saves can be transferred between devices and even OS's, no problem :) Make sure you grab the entire folder, including the "persistent" file, though!
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There's a file in the save folder called "persistent" and it contains all the persistent data (ie. data that persists even outside of your individual saves) such as Gallery unlocks.
A lot of people, when moving saves, just move the individually marked save files and not the entire folder, which results in things like your Gallery being erased.