Here's the process:
Email email@example.com the following information: A scan of your competitor's card, your Aeroplan number, and a screenshot of some sort of Air Canada flight activity that you've taken within 1 year on your Aeroplan page.
*When I first sent the email in April 2014, my AB card was active. When I got a re-request email, they asked for a new scan, and at that point, my AB card was inactive. I explained that, and it didn't seem to be an issue.
**This process took a very long time: 82 days to be exact! Just be patient, and reply with all the information they request, even if it's a repeat.