I am not sure if your code above uses SharedObject class or not, especially because your code refers to setItem() and getItem() methods that are not members of that class. If not, try to implement SharedObject. It can store vaues per user according to documentation (http://help.adobe.com/en_US/FlashPla...redObject.html
However I am not sure what you mean by 'another desktop'. A different login on the same windows or a different computer? If the latter is your case, the use of a remote server is inevitable. For this approach you can use a big number of client/server solutions, most simple and easy to implement imo is to call a web page (php/asp whatever you are familiar with) and pass the data you want to store as url variables. When you want them back, you ask that same page to deliver them to you again.