I know it's not quite what you asked for, but the more I thought about the workflow here, the more tortuous it became to do this inside email. You could have an OUTBOX shared via IMAP, but that exposes internal emails as well, which you didn't want; you could do it via mailing lists, but then everyone has to remember to cc the list; you could do it by getting the MTA to auto-cc mails between group members and the outside world - but it's highly MTA-dependent and some of them (eg sendmail) really quite resist doing it.
Assuming that there's a particular business function that this group services, may I suggest rethinking the problem and using a ticketing system like RT? RT's pretty simple to spin up, and a lot of my clients have got a lot of value out of one. Yes, there's the leap of people having to use the tool for that business function, but once you've taken that, advantages include:
- new inbound emails automatically have a ticket created, and a (highly customisable) autoresponse sent to the sender
- inbound emails that are part of an existing issue are automatically added to the existing ticket flow
- a particular ticket shows all the correspondence in its history, but no other correspondence; it's much quicker to see context than sorting through a shared folder of the last year's emails in and out of the group
- but there are powerful search facilities when you decide that you want to know about (eg) all resolved issues we've had with FribbleCorp this year
- tickets are easy to merge when duplication happens
- the individual owner of a particular problem is easy to see at any one time, which isn't obvious from an email correspondence
- tickets can be quickly and simply transferred from one person to another as tasks are completed and responsibility passes on
If you don't like RT, and there are those who don't, there are other lighter-weight ticketing systems like Double Choco Latte, and many more besides. I really do recommend that you think hard about whether there's a better way to do this than fine-tuning an email system until it squeaks.
All the above software is free, of course.