is it possible to make a ubuntu hard drive portable with ubuntu already installed?

I installed ubuntu 20.04 on an external hard disk using gparted to make partitions and i did everything this said but i gave up on the E step (Install Grub onto the ESP partition) because i couldn't unmount the media volume of the thumb drive. From there i used ubuntu for a month at least and i've got some files that i don't want to lose so I'd prefer not to reinstall it. But the computer i use with this HD isn't mine (my school gave it to me for online school ecc) and someday i'll have to give it back. With other computers it doesn't boot because there is no grub bootloader in it. Is there any way to make it portable without loosing the files there are in it?

A "Persistent Ubuntu USB" may be what you are looking for. Check this out:

https://www.howtogeek.com/howto/14912/create-a-persistent-bootable-ubuntu-usb-flash-drive/

A snippet of what this is from the website above:

A Linux live USB drive is normally a blank slate each time you boot it. You can boot it up, install programs, save files, and change settings. But, as soon as you reboot, all your changes are wiped away and you’re back to a fresh system. This can be useful, but if you want a system that picks up where you left off, you can create a live USB with persistent storage.

If you have a Windows PC handy, you can use LiLi USB Creator to make creating persistent storage for Ubuntu easier.

Let me know how it goes.