authorize different browsers to get the private data.

Flow:
The user jack logins in the website. The server validates  username and password, and generates a random code and saves it in an xml file, then sends the string of "validata:true;checkcode:FGHHKKKEYN" to the client. The client saves the value in cookie.  Within 30 days, when the client requests the private data, the server will validate the value from the client and the one saved in the XML file .
Problem:
Jack logins in the website by IE browser. Then he logins in by FireFox browser, the check code will be changed. So that Jack can't get private data before the cookie expires.
How to solve it?
Thank you.