llncs class uses a different way of defining theorem-like environments, so it's not a surprise that the other suggested methods don't work. Neither
ntheorem based solution can work.
Here I assume the theorem to repeat precedes the repetition. I define a new environment
reptheorem that stores the text; it has a mandatory argument that also sets a
\label with the same name.
In the example I also show that the optional argument is honored.
Let $x$ be a foo. Then $x$ is also a baz.