This tutorial is useful for the post-install setup of Exchange 2010.

After you set the Send Connectors and publish the MX records in DNS ( so that other email systems can find the server ) you have to configure the Exchange Server to receive e-mails.
The Hub Transport Server in Exchange is configured by default to not allow other systems to send emails to it. This default configuration is made to encourage the Edge Transport Servers to be set up for receiving mail, because it has a lot of security features that should be used in all organizations.

But, if you have an fresh install, and plan to use an Exchange Server without an Edge Transport you have to change the permissions on the receive connector for the Hub transport servers, using the tutorial bellow:

A. Configure Receive Connector Permissions Using the EMC ( Exchange Management Console )

1. Open EMC ( Start / All Programs / Microsoft Exchange Server 2010 / Exchange Management Console ):

2. Expand Server Configuration ( from the left menu ), and click on Hub Transport. Then right click on the Default Receive Connector, and select Proprieties:

3. After the Proprieties box appears go to Permission Groups Tab, and select Anonymous users, then click OK:

And now the Receive connector is ready to receive e-mails from other Mail Systems.

B. Configure Receive Connector Permissions Using Exchange Management Shell

1. Open Exchange Management Shell ( Start / All Programs / Microsoft Exchange Server 2010 / Exchange Management Shell )

2. Run the following command:

Get-ReceiveConnector “Default WIN-9A156E4DEJN” | Set-ReceiveConnector -PermissionGroups AnonymousUsers, ExchangeUsers, ExchangeServers, ExchangeLegacyServers

*Replace
WIN-9A156E4DEJN -> with the name of you server

ENJOY.

And if you encounter any problems feel free to comment / contact me.