I have transferred multiple Garmin mapsets to other notebooks often.
My method - involves registry modification - use at your risk.
Copy the entire mapset folder to the new computer. It needs to be in the same drive letter and folder name or you WILL have to edit the registry *.reg file.
e.g. mine are all under D:\GPS\Garmin\MapSource\xxxxx
Run regedit and navigate to/search for:
Windows 7 x64 - [HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Garmin\MapSource]
Windows 7 & XP x32 - [HKEY_LOCAL_MACHINE\SOFTWARE\Garmin\MapSource]
Export the section to a .reg file
Edit the .reg file CAREFULLY if your new PC is a different OS, drive or path. Remove "Wow6432Node\" for x32 or add for x64
Copy that .reg file to the new PC and double mouse click to add the entries to the registry.
Cross fingers and IF you have done it correctly it SHOULD all work.
Perhaps someone has perfected an automatic method?