How to hook to solution environment of exam class to put the answers in the end of document

Question

I want to put the answers to the end of the document, just like the way Martin Scharrer did in his reply to the question tex core - Showing Solutions of the Questions "separately" - TeX - LaTeX Stack Exchange, I can now put the answers of "true or false" kind of questions, and the answers of multiply choices questions, but I don't have a method to put the answers wrapped by solution environment of exam class.

Here is my code

%\documentclass[answers,12pt]{exam}
\documentclass[12pt]{exam}
\usepackage{environ}
\usepackage[normalem]{ulem}
\usepackage{etoolbox}

\usepackage{amssymb}
\newcommand\False{$\times$}
\newcommand\True{$\checkmark$}


\newlength\answerspace
\setlength\answerspace{0.5in}
\newcommand\dottedanswerline[1][{}]{%
  % One optional argument, the default value of which is empty.
  \unskip\linebreak[0]\enspace
  \hbox{}\nobreak\dotfill
  \ifprintanswers %whether to show the answers or leave it as a blank
    \hbox to \answerspace{(\hfil#1\hfil)}%
   % \xappto\answertext{\expandonce{\thequestion\theanswer}}
   %\xappto\answertext{\thequestion,#1\space}
  \else
    \hbox{(\hskip 0.5in)}%
    \xappto\answertext{\thequestion,#1\space}
  \fi
}% dottedanswerline


\newcommand{\answertext}{}
\usepackage{etoolbox}
\NewEnviron{answer}{\xappto\answertext{\expandonce{\BODY}}}%


\makeatletter

\AtEndEnvironment{solution}{\xappto\answertext{\BODY\space}}
%\AtEndEnvironment{solution}{\xappto\answertext{\thequestion,\BODY\space}}

\newlength\choiceitemwidth
\newif\ifshowsolution \showsolutiontrue
\newcounter{choiceitem}%选项的序号计数单元

\def\thechoiceitem{\Alph{choiceitem}}%用ABCD来显示选项序号

\def\makechoicelabel#1{#1\uline{\thechoiceitem.}\else\thechoiceitem.\fi\space} %答案显示下划线+字母或者字母，用于最终显示

\def\choice@mesureitem#1{\cr\stepcounter{choiceitem}\makechoicelabel#1}%计数器加1，同时显示ABCD标签，是用于测量长度的

%这个是用来进行测量用的，第一遍\BODY的parse
\def\choicemesureitem{\@ifstar
  {\choice@mesureitem\ifprintanswers \xappto\theanswer{\thechoiceitem}}%
  {\choice@mesureitem\iffalse}}%

\def\choice@blockitem#1{%
  \ifnum\value{choiceitem}>0\hfill\fi
  \egroup\hskip0pt
  \hbox to \choiceitemwidth\bgroup\hss\refstepcounter{choiceitem}\makechoicelabel#1}

\def\choiceblockitem{\@ifstar
  {\choice@blockitem\ifprintanswers}%
  {\choice@blockitem\iffalse}}

\def\choice@paraitem#1{%
  \par\refstepcounter{choiceitem}\makechoicelabel#1}

\def\choiceparaitem{\@ifstar
  {\choice@paraitem\ifprintanswers}%
  {\choice@paraitem\iffalse}}


\NewEnviron{mychoices}{%
  \def\theanswer{}
  \begingroup
    \let\item\choicemesureitem
    \setcounter{choiceitem}{0}%
    \settowidth{\global\choiceitemwidth}{\vbox{\halign{##\hfil\cr\BODY\crcr}}}%
  \endgroup 
  \dottedanswerline[\theanswer]
  \trivlist\item\relax
  \parindent0pt
  \setcounter{choiceitem}{0}%
  \ifdim\choiceitemwidth<0.24\linewidth
    \choiceitemwidth=0.25\linewidth
    \let\item\choiceblockitem
    \bgroup\BODY\hfill\egroup
  \else\ifdim\choiceitemwidth<0.48\linewidth
    \choiceitemwidth=0.5\linewidth
    \let\item\choiceblockitem
    \bgroup\BODY\hfill\egroup
  \else % \choiceitemwidth > 0.5\linewidth
    \let\item\choiceparaitem
    \BODY
  \fi\fi
  \endtrivlist

}
\makeatother



\begin{document}
\section{True OR False questions}
\begin{questions}
\question text text text text text text text text text text text text.\dottedanswerline[\True]

\question text text text text text text text text text text text text.\dottedanswerline[\True]

\question text text text text text text text text text text text text.\dottedanswerline[\False]
\end{questions}


\section{Multiply choices questions}
\begin{questions}
  \question Why is there air?
  \begin{mychoices}
    \item To blow up volleyballs.
    \item*  To fill an unneeded void.
  \end{mychoices}

  \question text text text text text text text text text text text text text text text text text text text text
  \begin{mychoices}
        \item foo
        \item bar
        \item*baz
  \end{mychoices}

\end{questions}

\section{Other questions}
\begin{questions}
\question[5] text text text text text text text text text text text text text text text text?
\begin{solution}[2cm]
1, text answer1
2, text answer2
\end{solution}

\question text text text text text text text text text text text text text text text text?
\begin{parts}
\part[2]
part one?
\part[2]
part two?
\end{parts}
\begin{solution}[2cm]
1, answer to part1
2, answer to part2
\end{solution}
\end{questions}
\section{Answers}
% \newpage
% Some time later
\answertext

\end{document} 

And here is the screen shot, I just want to put the answers(in blue color) in the end of the document. Those answers are put in the solution environment defined by exam class, so I try to use the \AtEndEnvironment{solution}{\xappto\answertext{\thequestion,\BODY\space}} command to append the body of the solution environment to the global variable, but surely \BODY is not defined.

Another improvement is that I need to put different kind of answers in different paragraphs, not in the same line as currently shown in the image.