The puzzle gets more confusing.

The spam shows that it was accepted by my Demon server. This is set up to forward
the mail to the account (on a different domain) on my SME server.. However....
There is no trace of the exchange between my demon server (or any demon mail server), and
the SME box. Nor of the POP3s exchange between SME and the user's machine. - Very odd.
There are no X-Spam-Check-By , X-SPam-Status or X-Virus-Checked headers (as shown by Thunderbird).
I have treble checked. There are two mail accounts on the user's machine, the new one she is using and an old one
to my demon server that is disabled. Not only has the old account been disabled by turning off all automatic attempts
to collect mail, I have changed the user name, so it
cannot work. Forcing its use, prompts for the password.
But I am still suspicious. The spam just received was dated in mid March and early April. Could it have arrived back then and only now
appeared? If so, it would have been handled by the demon server directly and that would agree with the headers.
I don't know if it is relevant but user reports that she often has "server cannot be reached" errors. She tries again
and gets through. I put this down to slow DNS.
I have checked and her machine resolves the external name of the SME server to the correct IP.
And the SME server's POP3s logs show here coming in at about the times we thought.
Ideas anyone? I'm stumped.
Ian