For future reference - the PGN data is stored in the /opt/picochess/games directory of Picochess.
However, to get the data directly from the board, DGT had(?) an app name: RabbitQueen that will download the PGN data from your board.
I no longer see it listed in the "unsupported" software section on the DGT website.
The app is a bit temperamental to get it to connect, just keep scanning the port.
My understanding is the data remains on the board until it fills up and then it is overwritten. The board does not have to stay in a powered up state.
*Disclaimer... I know nothing about the link I provided, so be careful.