net.lutris.lutris_0.5.2-2_amd64.deb

After installing Linux, when I installed the above package for the first time, Internet connection was necessary because the package had to download something from the Internet. After the installation had been completed, I disconnected Linux from the Internet and reinstalled the same package. This time the package was installed successfully without Internet connection. It goes to show that the downloads were still on Linux, so the package need not download them again. Where are the downloads on Linux. How can I find them? I want to back them up.

The "~/Downloads" folder is empty.

it depends on the tool you used to download. What OS is it? How did you download that file exactly?

My OS is UnionTech OS Desktop Home.
I just double-clicked on the said Debian package, which started downloading.
I downloaded the package by running the following command from Terminal:

I see. In that case probably this helps: https://unix.stackexchange.com/quest...pt-get-command

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Debian based systems will download files to /var/cache/apt/archive if memory serves me, and then install them from there. This is the same for command line apt usage or any of the various graphical packages.
They stay there until the "apt autoclean" command is run which deletes all the downloads, which some of the graphical tools when they are done.

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I'm extrapolating from what I see on one of my RaspPis so your situation may be somewhat different. I see downloaded packages in:

/var/cache/apt/archives

What do you see in that directory?

A brute force search for the package file beginning at '/', ought to find out where it 'lives':
should show you where it is (the above command redirects the inevitable permissions errors to the bit bucket). It could take a minute or more to complete so... patience.

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+1 for find. But doesn't it need the -xdev switch (plus a list of relevant file systems from df), to avoid endlessly traversing /sys, /proc, /dev, /run e.g. ???

I apologize for my stupid mistake.
I did not realize that I had already backed up all the dependencies required by the following package:

net.lutris.lutris_0.5.2-2_amd64.deb

As long as I have already installed all the dependencies, the package need not download anything and thus Internet connection is unnecessary.
In case I have not installed the dependencies, the package has to download them into the following folder:
/var/cache/apt/archives/