I have some E-Mails without a Date header in an Inbox. That's why they appear incorrectly in my MUA (Mozilla Thunderbird). So I would like to fix this.
There is an extension, with which I could manually edit the headers of a message. However, what it really does, is creating a new message and deleting the old one.
Is there a method to modify a message via IMAP or in another way generally?
How could I use that method, without manually talking to the server.
No. IMAP messages are immutable, by definition. If they were not, nothing would know whether they needed to resync them or not.
From RFC 3501, 2.3.1.1, statement 4:
4) The combination of mailbox name, UIDVALIDITY, and UID
must refer to a single immutable message on that server
forever. In particular, the internal date, [RFC-2822]
size, envelope, body structure, and message texts
(RFC822, RFC822.HEADER, RFC822.TEXT, and all BODY[...]
fetch data items) must never change. This does not
include message numbers, nor does it include attributes
that can be set by a STORE command (e.g., FLAGS).