Even if that is technically the keyboard that goes inside an A1181 topcase, you're not going to be able to install it without completely destroying the topcase. Like Mayer mentioned, the topcase is basically melted together in dozens of places, and taking it apart would make it unusable.

Any A1181 topcase will work on any A1181. I have about 200 or so various A1181 topcases, and I've never had a problem with any of them working on any of at least 100 A1181 MacBooks I've come across over the last year. Of course, there's a first for everything, and a surprise around every corner, but so far this rule has held true.