Can I transfer an installation?
A straight copy-paste of the whole installation folder should work. If you want to copy user-specific data as well, it should be in (My) Documents/Starcraft II.
Blizzard is actually really good about making their installations copy/pastable. Don't remember about the original Starcraft, but Warcraft III, WoW and SC2 can all be moved by just copy/paste on the whole installation directory. Any registry stuff is recreated on the new machine if it doesn't already exist (Not sure if it's updated if there's an old installation)