I don't have the new Lenovo Nook tablet. But the previous Nook tablet was a pretty standard Android tablet.
When you use Files or My Files (a few Android tablets don't come with a Files app, but you can install one from the Play store), can you see both internal and the SD card? If so, you can move files that way.
And you should be able to use Windows Explorer to move files to the SD card. On my tablets, I move comics from Windows to the SD card.
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