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Some server send email without Date header, and Thunderbird doesn't recognize the date.So, I want to use following settings and add Date header.

local_header_rewrite_clients = permit_inet_interfaces, ermit_sasl_authenticated
always_add_missing_headers = yes

But postfix.org says this may break DKIM signatures.
Is there a way to add Date headers withoud break DKIM signatures ?
(My mail server using DKIM.)

Example of no Date header mail :

Return-Path: <xxxxxx@example.com>
X-Spam-Checker-Version: SpamAssassin 3.4.0 (2014-02-07) on example.net
X-Spam-Level: ***
X-Spam-Status: No, score=3.7 required=8.0 tests=CONTENT_TYPE_PRESENT,
 FROM_MISSP_EH_MATCH,IP_LINK_PLUS,ISO2022JP_BODY,ISO2022JP_CHARSET,
 MISSING_DATE,MISSING_MID,NORMAL_HTTP_TO_IP,ONEGAI,QENCPTR1,RCVD_IN_DNSWL_NONE,
 RCVD_IN_MSPIKE_H2,RENRAKU,SPF_HELO_PASS,SPF_SOFTFAIL,TO_NO_BRKTS_FROM_MSSP
 autolearn=no autolearn_force=no version=3.4.0
X-Original-To: xxxxx@example.net
Delivered-To: xxxxx@example.net
Received: from xxxxx.example.org (xxxxx.example.org [xxx.xxx.xxx.xxx])
 (using TLSv1.2 with cipher ECDHE-RSA-AES256-GCM-SHA384 (256/256 bits))
 (No client certificate requested)
 by example.net (Postfix) with ESMTPS id D53991D45
 for <xxxxx@example.net>; Wed, 5 Sep 2018 20:44:48 +0900 (JST)
DKIM-Filter: OpenDKIM Filter v2.11.0 example.net D53991D45
Received: from xxxxx.example.org (xxxxx.example.org [xxx.xxx.xxx.xxx])
 by xxxxx.example.org (Postfix) with ESMTP id 77EFF8DC01
 for <xxxxx@example.net>; Wed, 5 Sep 2018 20:44:48 +0900 (JST)
Received: (qmail 23991 invoked by uid 101); 5 Sep 2018 20:44:43 +0900
Received: from unknown (HELO xxxxx.example.org) (xxx.xxx.xxx.xxx)
 by 0 with SMTP; 5 Sep 2018 20:44:43 +0900
Subject: ---email subject---
From: ---email subject---
To: ---email subject---
MIME-Version: 1.0
Content-Type: text/plain; charset=ISO-2022-JP
Content-Transfer-Encoding: 7bit
X-Mailer: Bap Version1
---email body---

It doesn't really matter that your server uses DKIM. A DKIM signature is something added by the sender, and making one requires the sender's private key.

As a part of DKIM signing, the sender's mail server takes some headers, typically including the Date header, concatenates these, and cryptographically signs the result. If you change any of those headers, or add one that wasn't there, you change the concatenated string and the signature will be invalid.

The mail you show is not DKIM signed.

The short version is: You can't do what you ask about.