Exchange 2010 mailboxes can not send to 2003 mailboxes

PROBLEM
Now we installed a new Exchange 2010 server in the same domain as the exchange 2003 server and installed the CAS, Mailbox and Hub roles. Next we about to move 70 mailboxes to the new Exchange 2010 server. Everything looks fine, users with mailboxed on the Exchange 2003 server can send mail to users on Exchange 2010 server. But the users with mailboxes on Exchange 2010 server can't send mail to mailboxes on exchange 2003. These messages stay in the 'SmtpRelayToTiRg' queue with error : 451 4.4.0 Primary Target IP address responded with: "451 5.7.3 Cannot Achieve Exchange Server authentication" 
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SOLUTION 1
I installed a Windows 2007 Exchange server in to my 2003 environment this week. All went well apart from that the mail sending from the 2007 test mailboxes ended up in a queue called smtprelaytotirg. The error message given being 451 4.4.0 Primary Target IP Address Responded with (501 5.5.4 Auth Command Cancelled).
This queue is basically where 2007 is failing to deliver because it can’t route correctly.
The resolution in this case for me was easy. All the connectors were in place as they should be, but the transport for SMTP on the original master 2003 Exchange server had limited access to certain IP addresses.
I added the IP address for the new Exchange 2007 server and bang, 20 mins later the queue is empty.
Just a minor hurdle :) Oh, the other one to watch out for is making sure it can resolve either by IP or FQDN for the SMTP server, it’ll fail on netbios or just a single name. Anyone still relying on WINS needs shot in the face with a screw driver.

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SOLUTION 2
http://forums.microsoft.com/TechNet/ShowPost.aspx?PostID=1087732&SiteID=17

Integrated Windows Authentication was not turned on, on my Default SMTP Virtual Server.....WORKED FOR ME

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Unable to assign "Send As" rights to Organization Units in Microsoft Exchange Server 2010

http://btsc.webapps.blackberry.com/btsc/search.do?cmd=displayKC&docType=kc&externalId=KB21225

Configuring the Microsoft Exchange Server 2010 permissions for the administrator account fails with insufficient permissions for the Users container, or any Organization Unit, even when logged in as a domain administrator. Assigning Send As rights to specific users, or groups, works successfully.

PowerShell Command: Add-ADPermission -InheritedObjectType User -InheritanceType Descendents -ExtendedRights Send-As -User "BESAdmin" -Identity "CN=Users,DC=example,DC=com"
Active Directory operation failed on example.com. This error is not retriable. Additional information: Access is denied.
Active directory response: 00000005: SecErr: DSID-031521D0, problem 4003 (INSUFF_ACCESS_RIGHTS), data 0
+ CategoryInfo : WriteError: (0:Int32) [Add-ADPermission], ADOperationException
+ FullyQualifiedErrorId : DA172DD1,Microsoft.Exchange.Management.RecipientTa sks.AddADPermission

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http://www.blackberryforums.com.au/forums/microsoft-exchange/8554-exchange-2010-bes-5-0-x-install-guide.html

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http://www.chicagotech.net/netforums/viewtopic.php?f=7&t=14344

Blackberry offers an alternative for running that powershell command
1. Open Active Directory Users and Computers.
2. Select the View menu and ensure Advanced Features is checked.
3. Right-click the Domain Name or Organizational Unit where Send As permissions are needed and select Properties.
4. Click the Security tab.
5. Click Advanced at the bottom on the Security tab.
6. Select Add and enter your Blackberry Service Account name (for example, BESadmin) and select OK.
7. When the permissions screen appears, change Apply onto: to User Objects (or Descendant User Objects on Microsoft Windows Server 2008).
8. In the permissions box, scroll down and check the Allow box beside Send As and press OK.
9. Press Apply and OK to exit.
it worked for me...

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http://www.commodore.ca/windows/exchange/blackberry/how-to-install-bes-express-exchange-2010-single-server.html