Emails are statying @ Local for Primary Domain.

We have received the dedicated server login with WHM-Cpanel login.

Then we have created the account used unlimited resources with domain name as for ex. a.com .

And then we have uploaded the website & database & created the FTP / SSH accounts as routine. COZ need to check this PHP application on IP Based , once site works good then we will transfer the DNS for this.

Then we have added the one more domain for ex. b.com as a a Add-on in same account and transfer the DNS for this using our registrar , then created the email accounts and it worked fine. But Twist is
We have 2 domains : a.com ( still using IP based ) & b.com ( DNS Transferred to Dedicated server ) . When i send an email from add-on domain b.com to primary a.com then email sent but not received at actual Remote side. It stays @ Local.

Is it due to a.com domain configured in a whm account. what would be the solution for this.

Regards,
VK