I guess the title says it all.
I would like to save the pictures to my external drive to use it on my other OS.
It doesn't appear to cache any images. It saves the current background at /home/<username>/.config/ubuntu-tweak/lovewallpaper.jpg
I gathered this info using lsof
- it only saves the files it downloads in a temporary directory while downloading, then deletes it and replaces the current one with the next one.
Gather the backgrounds you want and copy that picture for each one.
I don't use this tool so I can't really say, but if I should make a guess I'd say have a look at /usr/share/backgrounds/.
/home/<user>/.local/share/backgrounds
. /home/<user>/.local/share
is the user's equivalent to /usr/local/share
.