I found the solution. Change following code in the file /wp-includes/class-mailer.php:
...
$rt = @mail($to, $this->encodeHeader($this->secureHeader($subject)), $body, $header);
...
$rt = @mail($to, $this->encodeHeader($this->secureHeader($subject)), $body, $header, $params);
...
to:
...
$rt = @mail($to, $this->encodeHeader($this->secureHeader($subject)), $body, "From: admin@" . $_SERVER['HTTP_HOST']);
...
$rt = @mail($to, $this->encodeHeader($this->secureHeader($subject)), $body, "From: admin@" . $_SERVER['HTTP_HOST'], $params);
...
for me it works.