I think your best bet here assuming your new server is running our latest release is as follows: 

1. Create domainA.com on the new server. 

2. Copy full backups of both domains to a temporary storage location on the new server. I recommend using robocopy to ensure it captures ALL of the account data. 

3. Copy the backed up user accounts into C:\SmarterMail\Domains\domainA.com\Users.

4. Log in to SmarterMail on the new server as a system administrator and use the ...>Attach User functionality to bring all user accounts online within domainA.com. 

5. When that has been done, you should then be able to add domainB.com as a domain alias for domainA.com if you have not already done so during domain setup. 

When you use the ...>Attach User functionality it should detect the older account data and config structure and convert the user to the newer formats. That usually completes pretty quickly but you can check on the status by navigating to your server's convert-status page like this: 

I do recommend you complete backups of the affected environments before getting started just to be safe though, and please don't hesitate to submit a ticket with us should you need any help. Have a good one!