How to wrap a figure in exam document?

wrapfig doesn't work in lists, and questions is just another version of a list. The following is a quick and dirty reimplementation of https://tex.stackexchange.com/a/453624/117050 to work with enumerate like lists instead of with itemize. It uses insbox just like @Bernard's answer, but shouldn't require a manual paragraph. It does only implement the code to wrap inside one question, not inside the next one, too.

EDIT: It now should support exam's points system, but I didn't test it thoroughly. You might come back and complain if it doesn't work out.

EDIT2: Streamlined the interface to be more like the one of \InsertBoxR, the new macro's name is \questionInsboxR and it takes an optional argument, two mandatory ones, and a second optional one. The first optional argument is like the one of \question, the two mandatory arguments and the following optional one are like those of \InsertBoxR.

EDIT3: Added \questionInsboxL, fixed behaviour of multiple \questionInsboxL/R usages inside one questions environment.

\documentclass[12pt]{exam}
\usepackage{graphicx,wrapfig,lipsum}
\input{insbox}
\usepackage{capt-of}
\usepackage[onehalfspacing]{setspace}
\usepackage{mwe}

\usepackage{etoolbox}

\makeatletter
%% Stealing some code from exam:
\def\mypointshandling
  {%>>>
    \if@bonus
      \def\padded@point@block{%
        \begingroup
          \@placepointstrue
          \bonuspoint@block
        \endgroup
      }%
    \else
      \def\padded@point@block{%
        \begingroup
          \@placepointstrue
          \point@block
        \endgroup
      }%
    \fi
    \if@pointsdropped
    \else
      \if@bonus
        \if@bonusqformat
          \ifx\ques@ref\@queslevel
          \else
            \setup@point@toks
          \fi
        \else
          \setup@point@toks
        \fi
      \else
        \if@qformat
          \ifx\ques@ref\@queslevel
          \else
            \setup@point@toks
          \fi
        \else
          \setup@point@toks
        \fi
      \fi
    \fi
    \global \MyIfPointsfalse
  }%<<<
\protected\long\def\myOargparse#1#2%>>>
  {%
    \@ifnextchar[{\myOargparse@{#2}}{#2{#1}}%
  }%<<<
\long\def\myOargparse@#1[#2]%>>>
  {%
    #1{#2}%
  }%<<<
\def\q@mark{\q@mark}
\newif\ifMyIfPoints
\newif\if@notfirstins
\protected\def\questionInsboxL%>>>
  {%
    \myOargparse{\q@mark}{\questionInsbox@a\InsertBoxL}%
  }%<<<
\protected\def\questionInsboxR%>>>
  {%
    \myOargparse{\q@mark}{\questionInsbox@a\InsertBoxR}%
  }%<<<
\protected\long\def\questionInsbox@a#1#2#3#4%>>>
  {%
    \myOargparse{0}{\questionInsbox@b{#1}{#2}{#3}{#4}}%
  }%<<<
\protected\long\def\questionInsbox@b#1#2#3#4#5%>>>
  {%
    \if@notfirstins
    \else
      \def\makelabel##1{\hss\llap{##1}}%
      \apptocmd\@itemlabel{\hskip\leftmargin}{}{}%
    \fi
    \ifx\q@mark#2%
      \question
    \else
      \global\MyIfPointstrue
      \patchcmd\@readpoints{\global\@placepointstrue}{\relax}{}{}%
      \question[{#2}]%
      \patchcmd\@readpoints{\relax}{\global\@placepointstrue}{}{}%
    \fi
    \if@notfirstins
    \else
      \patchcmd\@itemlabel{\hskip\leftmargin}{}{}{}%
      \let\makelabel\@mklab
      \@notfirstinstrue
    \fi
    \mbox{}%
    \vspace*{-\baselineskip}%
    \setlength{\leftskip}{\leftmargin}%
    \ifx\InsertBoxR#1%
      #1{#3}{\hskip-\leftmargin#4\hskip\leftmargin}[{#5}]%
    \else
      #1{\numexpr#3+1\relax}{#4}[{#5}]\par\hspace{\itemindent}%
    \fi
    \ifMyIfPoints
      \mypointshandling
    \fi
    \the\point@toks
    \ignorespaces
  }%<<<
\makeatother

\begin{document}
\begin{questions}
  \question[5]\lipsum[2]
  \questionInsboxR[5]{0}
    {%
      \parbox[t]{.3\linewidth}
        {%
          \centering
          \includegraphics[width=\linewidth]{example-image-a.png}%
          \captionof{figure}{This is A}%
        }%
    }[1]
    Hello, I want to wrap this figure in exam
    \lipsum[1]
  \questionInsboxL[5]{2}
    {%
      \parbox[t]{.3\linewidth}
        {%
          \centering
          \includegraphics[width=\linewidth]{example-image-a.png}%
          \captionof{figure}{This is A}%
        }%
    }[1]
    Hello, I want to wrap this figure in exam
    \lipsum[1]
\end{questions}
\end{document}

Here is a solution with caption and the plain TeX insbox macro package. It defines a \InsertBoxR command, to be inserted at the very beginning of a paragraph, which takes two mandatory arguments: the number of untouched lines before a box id inserted, and the inserted box itself. In addition, in case TeX has a wrong computation of number of the necessary shorter lines, it accepts as an optional argument the number of supplementary shorter lines that you want.

\documentclass[12pt]{exam}
\usepackage{graphicx,wrapfig,lipsum}
\usepackage[onehalfspacing]{setspace}
\usepackage{mwe}
\usepackage{caption}
\input{insbox}

\begin{document}

\begin{questions}
\question
Hello, I want to wrap this figure in exam. \par
\InsertBoxR {0}{\parbox{0.3\linewidth}{\includegraphics[width=\linewidth]{example-image-a.png}\captionof{figure}{This is A}}}[3]
\lipsum[2]\lipsum[1]
\end{questions}

\end{document}