On Windows 7 or Windows 10, if I open IE and go to Twitter.com and log in clicking the Remember Me checkbox, log in and log out again, it does indeed Remember Me - my username is stored.
However, if I go into Internet Options → Browsing History → Settings → View Files there is no cookie visible there for twitter.com - there are only cookies for Microsoft sites (eg: cookie:kim@ieonline.microsoft; cookie:kim@bing)
I have searched the hard drive in other locations but cannot find any cookie from twitter on the filesystem. Can anyone tell me where the 3rd party cookie is stored?