Looking at my registration email versus my system registry, your license information is in the form of:UserName
The values are retrievable from:HKEY_CURRENT_USER\Software\mIRC\UserName
You should complete the normal About > Registration process rather than copying the system registry from one computer the another.
You should ignore the Validated key as it is unique to that system will be generated on its own following the normal registration process.
You can do a Portable install so you don't have to worry about this in the future as it will be stored in mirc.ini
You should write this information down into a leather bound book that includes all your passwords and software licenses, stored in your fire safe.