Ah. That's probably it.
Start installing the game (just a couple of seconds so it can create the right folders in Users/username/Appdata/Local.
Then close the launcher.
Go to the user folder of the previous account where the game was installed, copy (or cut) both "Frontier Developments" and "Frontier_Developments" directories and paste them to the new user's Local folder.
When you start the launcher then, it should see the game as installed. (To be sure go to Options in the Launcher and click "Validate game files" so it can check the data and potentially re-download/repair missing data.