Well, whatever you're talking about will be client-side.
You can easily send the e-mail to several addresses from your original PHP-script, I assume you understand that.
The ''forward'' function belongs exclusively to the e-mail client, and cannot be controlled by the e-mail itself (to my knowledge). It may be possible to insert some sort of form into the mail body, though. This, however, will most certainly not work on all e-mail clients.
I.e. (this is just THOUGHTS, I have never tried);
<form action="http://your.host.com/forwardMail.php" method="post">
<input type="hidden" name="mailContents" value="<mail contents>">
<input type="submit" value="Forward this message">
</form>
(you may be able to use javascript to get the mail contents dynamically, put the in a div tag and use divname.innerHTML)
Then write forwardMail.php to send a new e-mail to a designated address. The contents would obviously be whatever is in $mailContents (from the form). I'm not sure if this will work, but it's an idea.
Alternately, I'd say a better way to go is just send the e-mail to both addresses at once. There may exist some header like Forward-to, so you can make the client have a default forward address, but I've never seen one.
Good luck 😉