2 email server - 1 address - 1 inbox

[pipoy]

I run 2 servers.

1. Email server
2. Application server - E-commerce website

Both have the same email address
info@email.com
Application server sends system emails to my customers if ever they register, or buy something.
And I, as admin, receive emails from the system as well

I configured the DNS settings in my domain registrar to have the email, info@email.com, to receive by Email Server.
So far that is working well.

If you send an email to info@email.com - Email server receives it
If you are the customer and replied to the system emails, info@email.com - Email server receives it

However, if Application Server sends an email to info@email.com, it goes to its own inbox in Application Server.
So scenarios,
If system sends admin email to info@email.com - It goes to Application server inbox
If emails are bouncing - It goes to Application server inbox.

I want a solution where I can have both Inboxes in email server.

I fixed this issue by using an external SMTP server for the Application server. But website becomes slow if it tries to send an email. Perhaps because of connection and authentication. So I want to get away from that

So I think this is just a TXT or SPF or MX record setting issue. Which I hope someone can help me resolve.