No, FPS will not be improved by installing games on an SSD instead of on an HDD.
As you've already been told, there's no increase in game performance, the game will just load faster compared to installing it on an HDD.
Good FPS rates depends on the capabilities of other components (GPU, CPU etc), not the storage medium.
When deciding where to install games though, you need to remember that games can quickly swallow up the relatively low capacity of an SSD (compared to an HDD). So think about that when installing a game.