The \encl
name - what you see as \encl
in the output - is set within \enclname
. You can change it's formatting with something like
\renewcommand{\enclname}{\itshape encl}
in your preamble, together with
\encl{\itshape Important document}
inside your document code:

\documentclass{letter}
\signature{First Last}
\address{Source address}
\renewcommand{\enclname}{\itshape encl}
\begin{document}
\begin{letter}{Destination address}
\opening{To Whom it May Concern:}
This is the body of the letter.
\closing{Sincerely,}
\encl{\itshape Important document}
\end{letter}
\end{document}
However, there is really no need for the letter
class, since you can achieve the same output using article
, and it provides a similar-looking output:
\documentclass{article}
\pagestyle{empty}
\setlength{\parindent}{0pt}
\begin{document}
\vspace*{50pt}% Leave some space from the top of the document
\hfill
\begin{tabular}{l @{}}
Source addres \\
\\
\today
\end{tabular}
\bigskip
Destination address
\bigskip
To Whom it May Concern:
\medskip
This is the body of the letter.
\bigskip
\hspace{.5\linewidth}%
\begin{tabular}{ l }
Sincerely, \\
\\[2\bigskipamount]
First Last
\end{tabular}
\bigskip
{\itshape encl: Important document}
\end{document}
With the article
approach, you have free range to change content formatting.