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With \bgroup and \egroup instead of the braces: \documentclass{article}
\usepackage{ntheorem}
\newsavebox{\mybox}
\newenvironment{myenviron}{%
\savebox{\mybox}\bgroup}{\egroup%
\usebox{\mybox}}
\begin{document}
\begin{myenviron}
This is a test.
\end{myenviron}
\end{document}


This is how we ...