You were just right: that's simply a diagonal cross at the end of the object's lifetime.
From UML 2.5 p. 713:

Basically you just put that centered on the dashed life line below the execution. Then of course it means that at that point in time the object is no longer existent and will neither accept nor send any message. For your picture it might be (I have to guess without knowing details!) be the Login form
to terminate when Correct
part is executed and the Home page
comes into existence. As a side note I would use a createMessage

to actually create the Home page
instance right at that point.
As a second side note: don't try to use SD as graphical programming tool. Best stay away from fragments as long as possible. Better you create several diagrams that show a distinct flow of events in a fixed context. That would be one diagram for the positive login and one for the negative attempt. Of course both are trivial cases and you would not need them - they are for academic purpose only. SDs are useful to bring light into complex collaborations. With a stress on complex.