Launch the install, pause the download, copy the files, the files will be checked and the download will be finished instantly.
This doesn't work with data being delivered via SteamPipe: games being downloaded are temporarily installed, as "dummy data" that is gradually overwritten, to steamapps\downloading\[app id], rather than each of the files being downloaded in parts and, when complete, moved in full to steamapps\common\[installation directory], which was the case in the past. The only way to bypass Steam re-downloading a game is to have the installation directory in place before you install via the client, as it'll look for existing data before determining what to download.
Edit: Clarity.