Send emails from Exchange to external recipient with the same domain name

I have two mail servers - one of which is on Exchange. Both mail servers have the same domain name, let's say domain.com.

On the Exchange Server I have distribution list groups, but I need to add members which are from the external mail server with the same name, domain.com.

I can add users from other domains and add them to the distribution lists and they receive group mails fine. The problem is that If I add a mail recipient from the external domain.com mail to a group, they don't receive these mails. I guess that Exchange is trying to look for them inside his own mails.

Is it possible to make some sort of a rule for individual mails, which are on the external domain.com, so that they can receive these mails? I don't have that much mails so I can add an individual rule for each external mail.

If you've already configured the Accepted Domain for domain.com to be InternalRelay and created the Send Connector to route domain.com to the other mail server as suggested by @joeqwerty then your Exchange server should already be able to send email addressed for @domain.com addresses that are not local to it.

So now your remaining issue is how to add those addresses to Exchange such that you can add them to the required Distribution Lists.

To achieve that you want to use Mail Contacts. See Create a mail contact for the full description and how to set one up in EAC or via EMS.

With Exchange Distribution Lists you can only add mail objects that exist within Exchange, so typically those would be email accounts on the server. But for external addresses you can add them by creating a Mail Contact within Exchange, which specifically has a field for External email address which is not then treated as local. Create Mail Contacts for all the people you need to add to the distribution lists, using their email addresses on the second mail server, and then add them to the Distribution Lists as required.

When an email is processed by the Distribution List, Exchange will send to those contacts, see that they're not local, and then per the Accepted Domain and Send Connector rules will route any of the addresses it doesn't control locally to the other mail server.

Also remember that if those users will need to email that distribution list, they will be considered "external", so within the Distribution List Settings you'll need to enable the Allow people outside of my organisation to send email to this Distribution group option.

Agree with the above. you could create mail contacts. this will allow Exchange to recognize the external email addresses as valid recipients for the group emails.