doxendine It is strange that the same MoodleBox, v3.5.1 (30 Nov 2019), should run on only old RPi 4 B but not on a current 4 B. What exactly is the difference. Does the SD card refuse to boot? Or does it boot and throws an error message on the console? If so, what is the message? (Connect a monitor to the RPi.)
I notice that 3.5.1 is still Rasbpbian and from 3.6 it is the RaspberryPi OS. I wouldn't know what difference that should make.
Anyway, to continue with a site in that old MoodleBox on a new RPi 4 B, the safest is to make a fresh (4.3.0) MoodleBox and migrate the Moodle site from the old MoodleBox to the new one. That is exactly what the link Ian posted does, specific to MoodleBox. The original documentation generic to Moodle is https://docs.moodle.org/en/Moodle_migration.
Yes, course-wise https://docs.moodle.org/en/Course_backup and https://docs.moodle.org/en/Course_restore is an alternative, but it is not exactly the same.
About copying the files, haven't we discussed it and you've found a solution https://discuss.moodlebox.net/d/318-share-multiple-files-at-once ?