Restoring apt cache

My laptop will not boot.  I have been trying to get its HDMI output working
and something awful happened and now it will not boot. Oh dear, how sad, I
can cope. I have my bootable USB stick so can recover.

But I am a long way from a decent internet connection so do not want to
reinstall all my software over the net.  I have managed to burn my
/var/cache/apt onto a DVD (that was not easy) and I would like to know can
I expect to reinstall, which will stomp that cache(?), and copy the
cache/apt into the fresh file system and will those packages be available
to me without having to download again?

It seems to me that it should, but it is the first time I have tried.  I
know my /home directories will endure over reinstalling from my stick, but
the /var hierarchy? And if not I do not know if there is more I need to do
to copy my old packages over.

Since my last install (I reinstalled Ubuntu in the hope HDMI would work
better from there) I have not cleared the cache.

cheers
W

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