See if either of these helps out:
https://twinery.org/questions/1102/how-to-transfer-variables-from-one-twine-story-to-another
https://twinery.org/questions/1274/how-i-can-transfer-choices-from-one-story-to-other-sugarcube
Both questions have multiple answers based on your needs and preferences.
It's not but the code still works and is all there. Should be easy enough to test yourself, but I can see if I still have it to reupload if you need me to.
Also, is there a way to do this locally on the player's machine?
The local storage route should work for that. The original method I posted there won't. The postmessage API answer should also work, though I haven't personally tested it.