Nkduodu I am having trouble in understanding your question. You said,
instead of giving each student a MoodleBox i rather want each student to "own an SDHC card with all their details and raspian installed on the SDHC card"
So the SD card is Raspbian, now called Raspberry Pi OS? Then you are indeed in the wrong forum.
When they come into the lab, they insert their SDHC and boot up and then connect to the "MoodleBox Server."
Then the Raspbian is the client computer (also called desktop)? The "MoodleBox Server" is something else, a central Raspberry Pi with a MoodleBox SD card - owned by you, the teacher, perhaps? Then all the work the student does on that Moodle lands automatically in that Moodle. I don't see what you want to backup?