OK, it was quite easy. After having plugged in the USB cable and connected the tablet to the computer, then under Settings -> Attached Devices -> USB, just click on USB, then a dialog window pops up, titled "Use USB For", and then you select "Transfer Files". After that the tablet's filesystem will be accessible in Linux when you mount it. Note that all the menu names are translated from Danish, so I am not 100% sure that they match the English original completely.
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