I need a way to export a stashed change to another computer.

On computer 1 I did

$ git stash save feature

I'm trying to get the stash patch to a file and then import it to another computer

$ git stash show -p > patch

This command gives me a file that I can move to another computer where this repo is cloned, but the question is how to import it as a stash again.

You can apply a patch file (without committing the changes yet) by simply running

git apply patchfile

Then you can simply create a new stash from the current working directory:

git stash