For one thing, even if you do reply to that old message, Mailman will still show your email in the month it was sent. So it's probably not worth the hassle to try replying to a message you don't have. Just send a new email out to the mailing list with your solution (assuming it is topically relevant).
However, for educational purposes: copying the subject won't be enough, because not every message on a mailing list can be expected to have a unique subject. The standard way to indicate that you're replying to a message is through the email header
In-Reply-To. The value of that header is taken from the
Message-ID header of the message you're replying to. Normally this is done automatically by your email client, but if you use a program that allows you to set custom header fields, you should be able to do it manually. If you go to the list archives of the mailing list in question and click on the "Gzip'd text" link for the month in question, you should get a gzipped text file that includes the Message-ID headers for each email sent that month. Copy the value of the header from the message you're trying to reply to, and add a custom
In-Reply-To header with that value to the message you're sending. For instance, if you see
in the message you're replying to in the downloaded text file, you should add the custom header
to the message you're sending, and your message will then be considered a reply to the old message.