Spacing issue in new environment from a theorem

Question

I'm trying to create a theorem environment that I can use to repeat a theorem that has been previously stated in a book but number it the same as the 1st instance. I found some sort of solution:

\documentclass{article}

\usepackage{amsthm} 

\newtheorem{theorem}{Theorem}
\newcounter{thmC}
\newtheorem{rethm}[thmC]{Theorem}

\newenvironment{retheorem}[1]%
{\setcounter{thmC}{#1}%
\addtocounter{thmC}{-1}%
\begin{rethm}}%
{\end{rethm}\ignorespacesafterend}

\begin{document}

\begin{theorem}\label{theorem:Hi}
Hi this is my theorem.
\end{theorem}

\begin{theorem}\label{theorem:another}
Another theorem.
\end{theorem}

\begin{theorem}\label{theorem:third}
third theorem
\end{theorem}

\begin{retheorem}{\ref{theorem:third}}
third theorem
\end{retheorem}

\begin{retheorem}{\ref{theorem:another}}
Another theorem.
\end{retheorem}

\begin{retheorem}{\ref{theorem:Hi}}
Hi this is my theorem.
\end{retheorem}

\end{document}

It nearly works but there is a spacing issue.

My further concern is will this approach work for theorems labeled with the section

\numberwithin{theoremC}{section}
\newtheorem{theorem}[theoremC]{Theorem}

Answer 1

This functionality is already provided by the restatable environment from the thmtools package; the package also offers a continues key and it handles, in both situations, the case of the theorem counter being subordinated to another one:

\documentclass{article}
\usepackage{amsthm} 
\usepackage{thmtools,thm-restate}

\declaretheorem[numberwithin=section]{theorem}

\begin{document}

\section{Test section one}
\begin{theorem}[label=thm:key]
This is a theorem that will be continued later.
\end{theorem}
\begin{restatable}{theorem}{Hi}
This is my first restatable theorem.
\end{restatable}
\begin{restatable}{theorem}{another}
This is my second restatable theorem.
\end{restatable}
\section{Test section two}
\begin{restatable}{theorem}{third}
This is my third restatable theorem.
\end{restatable}
\section{Test section three}
\third*
\another*
\Hi*
\begin{theorem}[continues=thm:key]
And here I expand my theorem.
\end{theorem}

\end{document}

However, there's still a little difference in vertical spacing between the restatable and the standard theorems.