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I want to arrange that the recipient's address fits the window of the envelope in a simple letter-class letter (my address on top right, the date underneath and still on the right, then the recepient's address below that and on the left, then the opening below and the closing on the right at the end of the letter).

This question is about the same issue but using the class scrlttr2 (instead of letter), which is way too cryptic for me for such a simple task (I cannot work out how to make a "normal" simple letter out of the scrlttr2 class).

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I am not familiar with the standard letter class. So here is a suggestion for a letter using scrlttr2:

\documentclass[
  backaddress=off,% no backaddress above the recipients address
  foldmarks=off,% no foldmarks - maybe you want to use them
  refline=nodate,% no date in the refline
  %DINmtext
]
{scrlttr2}

\setkomavar{fromname}{Name}
\setkomavar{fromaddress}{Street Number\\11111 Town}

\setkomavar{firsthead}{%
  \raggedleft
  \begin{tabular}{l@{}}
    \usekomavar{fromname}\\
    \usekomavar{fromaddress}\\[\normalbaselineskip]
    \usekomavar{date}
  \end{tabular}
}

\renewcommand\raggedsignature{\raggedright}

\usepackage{blindtext}% dummy text

\begin{document}
\begin{letter}{Sun\\ Sun street\\ Sun town}
  \opening{Hello}
    \Blindtext[2]% filling text
  \closing{Best regards}
\end{letter}
\end{document}

enter image description here

Note that the position of the window depends on the country and the size of envelope. The default settings (DIN.lco is loaded automatically) are for German C4, C5, C6 and C5/C6 envelopes. There are some other lco files predefined, e.g. DINmtext.lco (German only C6 and C5/6), SNleft.lco (swiss), ... You can load them as class option without the postfix .lco.

It is also possible to adjust the position and the size of the address field to your needs, see scrlttr2: Position of the recipient's address

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