That's simple, Use browser cookies to store the same. So that next time the user logs in you can pick the value from the cookie in his browser .
IMPORTANT : BUT Here's how you make it secure.
Since you are storing the UserID etc. I would recommend encrypting and storing it, next time you can pic the value decrypt and then show back
OR
Just set a flag in cookie on click of checkbox (to remember) and populate the User ID and code from the server code if that flag is true the next time you see from cookie.
EDIT : Since you have not mentioned what language/tech you are developing this, just use server side api's to read the cookie values or jQuery/script