The request being made is not at all clear: if one just wants to typeset the labels of a description
environment as if they were part of an enumerate
environment, why should one use description
at all? Evidently, the question lacks some essential information. A possible interpretation is that what is actually wanted here is to typeset a regular description
-style label with a number sticking in the margin, with an alignment similar to that of the labels of enumerate
. The following example clarifies what I mean.
\documentclass[a4paper]{amsbook}
\usepackage[T1]{fontenc}
\usepackage{enumitem} % actually redundant, in this example
\newenvironment*{descriptionThatMimicksItemize}{%
\list{}{\let\makelabel\descriptionTMIlabel}%
}{\endlist}
\newcommand*{\descriptionTMIlabel}[1]{\hss\llap{\upshape #1}}
\makeatletter
\@ifdefinable\origLabelWidth{\newdimen\origLabelWidth}
\@ifdefinable\origLabelSep {\newdimen\origLabelSep}
\makeatother
\newcommand*{\myNumericLabel}[1]{%
\makebox[\origLabelWidth][r]{#1}\hspace{\origLabelSep}%
}
\begin{document}
\origLabelWidth = \labelwidth
\origLabelSep = \labelsep
% This is an over-simplification, but for now we can accept it.
The \texttt{enumerate} environment:
\begin{enumerate}
\item \label{a}
Lorem ipsum dolor sit amet consectetur adipisci elit iam
fugiaet enim duscula. Reprivit ursula tum donec.
\item \label{b}
Lorem ipsum dolor sit amet consectetur adipisci elit iam
fugiaet enim duscula. Reprivit ursula tum donec.
\end{enumerate}
The first solution:
\begin{descriptionThatMimicksItemize}
\item[(\ref{a}) Is it this what you want?]
Lorem ipsum dolor sit amet consectetur adipisci elit iam
fugiaet enim duscula. Reprivit ursula tum donec.
\item[(\ref{b}) I wouldn't say so.]
Lorem ipsum dolor sit amet consectetur adipisci elit iam
fugiaet enim duscula. Reprivit ursula tum donec.
\end{descriptionThatMimicksItemize}
The second one:
\begin{description}
\item[\myNumericLabel{(\ref{a})}I'd rather say it's this]
Lorem ipsum dolor sit amet consectetur adipisci elit iam
fugiaet enim duscula. Reprivit ursula tum donec.
\item[\myNumericLabel{(\ref{b})}A label is needed, though]
Lorem ipsum dolor sit amet consectetur adipisci elit iam
fugiaet enim duscula. Reprivit ursula tum donec.
\end{description}
\end{document}
Output:

If this is the real issue, it involves splitting the supplied label in two components, and therefore goes beyond the mere problem of setting the margins and the label width.
In conlusion, I think that it is impossible to fully answer this question until it is made clear what the precise request is.
Addition
I'm beginning to wonder whether it couldn’t be simply this what is actually wanted:
\documentclass[a4paper]{amsbook} % or whatever
\usepackage[T1]{fontenc}
\usepackage{hyperref}
\begin{document}
Let \( f\colon A\to B \) be a function. The following are equivalent:
\begin{enumerate}
\item\label{a} $f$ is both injective and surjective;
\item\label{b} $f$ is invertible.
\end{enumerate}
Proof:
\begin{enumerate}
\item[$\ref{a}\Rightarrow\ref{b}$:]
Pick an element \( b\in B \), and let \( a\in A \) be the unique element
that is sent into~$b$ by~$f$\ldots
\item[$\ref{b}\Rightarrow\ref{a}$:]
Lorem ipsum dolor sit amet consectetur adipisci elit iam
fugiaet enim duscula. Reprivit ursula tum donec.
\end{enumerate}
\end{document}
Output:

Of course, the hyperlins work as expected.
But indeed, this wouldn’t be worth a bounty…
Second Addition
Yet another possibility:
\documentclass[a4paper]{amsbook} % or whatever
\usepackage[T1]{fontenc}
\usepackage{enumitem}
\usepackage{hyperref}
\setlist[enumerate,1]
{align=left, labelindent=.5em, labelwidth=1.5em}
\begin{document}
Let \( f\colon A\to B \) be a function. The following are equivalent:
\begin{enumerate}
\item\label{a} $f$ is both injective and surjective;
\item\label{b} $f$ is invertible.
\end{enumerate}
Proof:
\begin{enumerate}
\item[$\mbox{(\ref{a})}\Rightarrow\mbox{(\ref{b})}$:]
Pick an element \( b\in B \), and let \( a\in A \) be the unique element
that is sent into~$b$ by~$f$\ldots
\item[$\mbox{(\ref{a})}\Rightarrow\mbox{(\ref{b})}$:]
Lorem ipsum dolor sit amet consectetur adipisci elit iam
fugiaet enim duscula. Reprivit ursula tum donec.
\end{enumerate}
\end{document}
And here is the output #3:

description
list? – Werner Apr 15 '15 at 21:26description
when you want an enumerated list? – egreg Apr 15 '15 at 21:40enumerate
-description
style environment – Werner Apr 15 '15 at 21:43