My guess--and it's just a guess. I'm assuming that since it's the client that picked up the script to run, it'll be similar to the same context that other scripts run in, when picked up by policies, like Configuration Item Scripts, or Scripts used for Detection Logic for Applications--which is NT Authority\System, of the individual device.
So if you want all your Domain Computers to have rights to some remote share, you'll want to make a share, and grant (I think) "Domain Authenticated Users" both NTFS modify to that location, and that the Share also has Modify rights to Authenticated Users. I think that might work...
I see you're trying to use s$... that would be an Admin share. I wouldn't use that. Make a real Share, which you can permission properly.