This question already has an answer here:
So I had my Steam game installed in
H:\Games and wanted to move it to
C:\Program Files (x86)\Steam\steamapps\common\.
I followed this Steam guide on how to move a Steam installation. I moved my game folder to a safe location while steam was closed. Then launched steam, right-clicked the game in the library, and deleted local content. I closed steam again, moved the backup game folder to my target location in the common folder. I opened steam and found the game greyed out as if it was not installed. I entered properties and could not verify the game cache. It prompted me to install. I installed it to the common folder and it was downloading. I tried to vertify it, but it did not vertify, just kept downloading.
The game is Borderlands 2.