grub rescue / move folder

If you have direct access to this machine (perhaps via this browser terminal popup thing (?)), you could try to load your kernel and the initramfs and boot it.

This won't bring up your system again (because the boot process doesn't only depend on /boot) but you can get into a shell.

If you have full access to GRUB this may work:

linux /<path>/boot/vmlinuz<...>
initrd /<path>/boot/initrd<...>

Because you haven't specified a root file system (via root=...) - because you currently don't have a usable one -, your system will run a busybox shell right from the initramfs.

This (initramfs) prompt is a complete shell. You need to create a folder - run mkdir /rootfs). Then you would need to mount your root file system (mount -o rw /dev/<...> /rootfs) and chroot into it (chroot /rootfs /bin/bash).

Then you can mount your other file systems (mount -a). Then you are able to do whatever you want.

Disclaimer: This is - as the question is, too - a cross-post from Super User.