Tried this recently, and it's a complete mess if you run low on disk space. When trying to move a 100GB game to the SSD recently it turned out that:
1) steam will not rediscover the files automatically at startup or by attempt to launch the game, nor is there any specific option
2) the existing file discovery process is instantiated by forcing a new download of the game
3) this process will not begin unless there is enough free space for the game
So in the end, I had to copy the files back to the HDD to make space on the SSD, start an install of the game on the ssd, exit steam, copy the files to the SSD again, open steam and resume download, then wait for it to verify each file.