PHP: Write non ASCII Characters like german umlauts (öäü)

Question

I'm programming a quite simple PHP Script, that writes a string (sentence) got from an HTML FORM into a file. This string sometimes contains Non-ASCII Characters, in my case german umlauts, äöü. But instead of writing them to the file correctly it just writes little question-mark-symbols.

How can I fix that?

<?php
header('Content-type: text/html; charset=utf-8');


#   $_POST["message"]
#   $_POST["random"]
#   $_POST["date"]

#$MESSAGE = utf_encode($_POST["message"]);

$countfile = fopen("filecount", "r");

$filecount = fread($countfile,filesize("filecount"));
fclose($countfile);


$filename = $filecount + 1;
echo($filename);

if ($_POST["random"]){

$newmessagefile = fopen($filename, "w");
fwrite($newmessagefile, $_POST["message"]);
fclose($newmessagefile);

$countfilew = fopen("filecount", "w");
fwrite($countfilew, $filename);

fclose($countfilew);
}


else {

    $newmessagefile = fopen($_POST["date"], "w");
    fwrite($newmessagefile, $_POST["message"]);
    fclose($newmessagefile);

    $specialdaysfile = fopen("specialdays", "a");
    fwrite($_POST["date"]);
    fclose($newmessagefile);

}

?>