I need to move an alternate domain name from a account I cannot access to my account

You're absolutely right. The error message "Alias move is not allowed since the source distribution is enabled" indicates that the domain (www.example.com) is currently associated with another Cloudfront distribution in a different AWS account. Unfortunately, transferring domains directly between AWS accounts isn't possible.

Here are the next steps you can take:

1. Contact the Current Account Owner (if possible): If you know who owns the other AWS account associated with the domain, try contacting them directly. Explain the situation and request that they disassociate the domain from their Cloudfront distribution. Once they disable it, you can then associate it with your own Cloudfront distribution.

2. Use AWS Support: As you mentioned, contacting AWS Support is a good option if you can't reach the current account owner. AWS Support can't directly transfer the domain, but they can help you work through the process. Here's what to tell them:

Explain that you're trying to associate your domain (www.example.com) with your Cloudfront distribution, but it's currently associated with another account. Provide evidence that you own the domain. This could include domain registration details, WHOIS information, or control panel access screenshots (if applicable). Request assistance in resolving the issue. AWS Support might be able to help you contact the other account owner or provide alternative solutions