To emphasize the answer to your direct question. As Adrian_Hills indicates, the backup.bat script will zip up everything you need. Copy that over to the openHABian and you can use openhabian-config or openhab-cli restore to restore the configs from the Windows to the Linux version.
In general a backup needs to include all of the conf folder and most of the userdata folder. You should be able to open the zip file created by backup.bat to see what it grabbed as part of the backup.
Note you will likely need to change COMM ports to /dev/ttyUSBX for any bridge Thing that uses a USB device (e.g. Zwave, Zigbee, etc.).