The llncs class uses an approach different from amsthm, therefore the other solution is not applicable.
Add the following lines to your preamble:
\newcommand\repeatedtheorem[2]{%
\expandafter\let\expandafter\repeatedtheoremtmp\csname#1name\endcsname
\expandafter\def\csname#1name\endcsname{%
\repeatedtheoremtmp\ \ref{#2}%
\global\expandafter\let\csname#1name\endcsname\repeatedtheoremtmp
}
}
To repeat the number of a theorem, you have to do the following things.
Define an unnumbered version of your theorem environment. E.g., if you want to recall/preview a theorem, add the following line to your preamble:
\spnewtheorem*{theorem*}{Theorem}{\normalshape\bfseries}{\itshape}
This will define an environment theorem* that looks like the theorem environment, but without numbers.
Add a label to the theorem whose number you want to reuse, say \label{myAmazingTheorem}.
At the place where you want to preview/recall the real theorem (with the number given there), use the unnumbered version \begin{theorem*}...\end{theorem*}.
Immediately before this unnumbered theorem, tell LaTeX to use the number of the real theorem by adding the line
\repeatedtheorem{theorem*}{myAmazingTheorem}

\documentclass[envcountsect]{llncs}
\spnewtheorem*{theorem*}{Theorem}{\normalshape\bfseries}{\itshape}
\newcommand\repeatedtheorem[2]{%
\expandafter\let\expandafter\repeatedtheoremtmp\csname#1name\endcsname
\expandafter\def\csname#1name\endcsname{%
\repeatedtheoremtmp\ \ref{#2}%
\global\expandafter\let\csname#1name\endcsname\repeatedtheoremtmp
}
}
\begin{document}
\section{Preview}
\repeatedtheorem{theorem}{myAmazingTheorem}
\begin{theorem}[just a preview]
My amazing theorem that we will discuss later.
\end{theorem*}
\begin{theorem}
An unnumbered theorem.
\end{theorem}
\section{The real thing}
\begin{theorem}[The Amazing Theorem]
\label{myAmazingTheorem}
A theorem
\end{theorem}
\end{document}