This sounds typical -- and correct. First, I must warn you against manually replicating address books, especially ones in different domains. The ACLs of those servers are set up for that domain. When you replicate them manually, you run the risk of overriding settings for that domain, such as the administration server. When you manually replicate the databases as a manager, you will pass the ACLs between the servers.
If you are a manager of both domains, you can troubleshoot the replication issues by investigating the ACLs and connection documents. In this case, it appears to be that domain B is not set to allow users from your domain A to access and use the server. If you want users and servers from the domains to be able to use each other, you need to cross-certify the domains, allow the domains to access each other's servers or both.
This was first published in April 2003