Saving and restoring changes of a Live system is not a built-in feature of VL, sorry.
Okay, forgive me for asking, but are we really sure about this? Persistence is built into Slax, and Vector Live 7 seems to be based on the Slax archtecture. I'm having trouble running the boot installer script, but when I tried to boot my USB, a third folder appeared in my

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It's always been my conviction that in SLAX, the "changes" folder is where persistence occurs.
What's more, if automatic persistence isn't possible, I'd expect that you should be able to make persistent changes directly by adding items to the "rootcopy" and "modules" folders.

Am I barking up the wrong tree here? For about two years, I had the fun of releasing my own live CD, a customized version of Slax, and it looks like I'm seeing all the familiar customization tools that I used during that time. So, if nothing else, I'd expect that you should be able to make persistent changes by editing the files on the drive.
I've got to think that this is already covered on this forum somewhere, but if not, and if this turns out to useful, I'll go into more detail later.