Is it possible to push a git stash to a remote repository?

It's not possible to get it via fetch or so, the mirror refspec is fetch = +refs/*:refs/*, and even though stash is refs/stash it doesn't get sent. An explicit refs/stash:refs/stash has no effect either!

It would only be confusing anyway since that wouldn't fetch all stashes, only the latest one; the list of stashes is the reflog of the ref refs/stashes.

Note: I've just rewritten this answer with 24 hours more git-fu under my belt :) In my shell history, the whole shebang is now three one-liners. However, I've uncondensed them for your convenience.

This way, I hope you will be able to see how I did things, instead of just having to blindly copy/paste stuff.

---

Here is step by step.

Assume is source in ~/OLDREPO containing stashes. Create a TEST clone containing no stashes:

cd ~/OLDREPO
git clone . /tmp/TEST

Push all the stashes as temp branches:

git send-pack /tmp/TEST $(for sha in $(git rev-list -g stash); \
    do echo $sha:refs/heads/stash_$sha; done)

Loop on the receiving end to transform back into stashes:

cd /tmp/TEST/
for a in $(git rev-list --no-walk --glob='refs/heads/stash_*'); 
do 
    git checkout $a && 
    git reset HEAD^ && 
    git stash save "$(git log --format='%s' -1 HEAD@{1})"
done

Cleanup your temporary branches if you will

git branch -D $(git branch|cut -c3-|grep ^stash_)

Do a git stash list and you will something like this:

stash@{0}: On (no branch): On testing: openmp import
stash@{1}: On (no branch): On testing: zfsrc
stash@{2}: On (no branch): WIP on sehe: 7006283 fixed wrong path to binary in debianized init script (reported as part of issue
stash@{3}: On (no branch): WIP on debian-collab: c5c8037 zfs_pool_alert should be installed by default
stash@{4}: On (no branch): WIP on xattrs: 3972694 removed braindead leftover -O0 flag
stash@{5}: On (no branch): WIP on testing: 3972694 removed braindead leftover -O0 flag
stash@{6}: On (no branch): WIP on testing: db9f77e fuse_unmount_all could be starved for the mtx lock
stash@{7}: On (no branch): WIP on xattrs: db9f77e fuse_unmount_all could be starved for the mtx lock
stash@{8}: On (no branch): WIP on testing: 28716d4 fixed implicit declaration of stat64
stash@{9}: On (no branch): WIP on emmanuel: bee6660 avoid unrelated changes

On the original repository, the same looked like

stash@{0}: WIP on emmanuel: bee6660 avoid unrelated changes
stash@{1}: WIP on testing: 28716d4 fixed implicit declaration of stat64
stash@{2}: WIP on xattrs: db9f77e fuse_unmount_all could be starved for the mtx lock
stash@{3}: WIP on testing: db9f77e fuse_unmount_all could be starved for the mtx lock
stash@{4}: WIP on testing: 3972694 removed braindead leftover -O0 flag
stash@{5}: WIP on xattrs: 3972694 removed braindead leftover -O0 flag
stash@{6}: WIP on debian-collab: c5c8037 zfs_pool_alert should be installed by default
stash@{7}: WIP on sehe: 7006283 fixed wrong path to binary in debianized init script (reported as part of issue #57)
stash@{8}: On testing: zfsrc
stash@{9}: On testing: openmp import