I am not quite sure I have understood your question. However I believe I
updated
https://trisquel.info/en/wiki/cloning-system-or-how-make-copy-installed-packages-one-computer-another
to answer it! :-)
Basically, you have to download again the DEB packages that are
architecture-dependent but you can still copy the remaining ones
(/var/cache/apt/archives/*_all.deb) from one system to the other and save a
little bandwidth.
https://trisquel.info/en/wiki/cloning-system-or-how-make-copy-installed-packages-one-computer-another
gives different ways how to manually transfer the files. However, since we
are talking about updates, 'rsync' would be appropriate. To only fetch the
/var/cache/apt/archives/*_all.deb files that are different. And you can
define an 'alias' (e.g., in ~/.bash_aliases, assuming you use Trisquel's
default shell to update your system and ~/.bashrc executes ~/.bash_aliases,
as it does by default) that would fetch the newest
/var/cache/apt/archives/*_all.deb files from the other computer and then
launch the update.
