After Migration Exchange 2013 does not send mail outside the organization

Question

Dear,
After Migration Exchange 2010 to exchange 2013. We does not send email from the organization but we can received mail from others organization.
Delivery has failed to these recipients or groups:
[email protected] ([email protected]) The server has tried to deliver this message,
without success, and has stopped trying. Please try sending this message again. If the problem continues, contact your helpdesk.
Diagnostic information for administrators:
Generating server: OGMAIL.domain.net Receiving server: gmail.com (2607:f8b0:400c:c01::1a)
[email protected] 6/11/2014 10:16:10 AM - Remote Server at gmail.com (2607:f8b0:400c:c01::1a) returned '550 4.4.7 QUEUE.Expired; message expired' 6/11/2014
10:03:49 AM - Remote Server at gmail.com (2607:f8b0:400c:c01::1a) returned '441 4.4.1 Error encountered while communicating with primary target IP address: "Failed to connect. Winsock error code: 10051, Win32 error code: 10051." Attempted failover
to alternate host, but that did not succeed. Either there are no alternate hosts, or delivery failed to all alternate hosts. The last endpoint attempted was 2607:f8b0:400c:c01::1a:25'
Original message headers:
Received: from OGMAIL.domain.net (192.168.10.12) by ogmail.domain.net
 (192.168.10.12) with Microsoft SMTP Server (TLS) id 15.0.847.32; Mon, 9 Jun
 2014 16:13:30 +0600
Received: from OGMAIL.domain.net ([::1]) by ogmail.domain.net ([::1]) with
 mapi id 15.00.0847.030; Mon, 9 Jun 2014 16:13:30 +0600
From: Administrator <[email protected]>
To: Administrator <[email protected]>
CC: IT.HW-Masudur Rahman-MRT <[email protected]>, "[email protected]"
    <[email protected]>
Subject: RE: Migration batch mrtmove has completed successfully.
Thread-Topic: Migration batch mrtmove has completed successfully.
Thread-Index: AQHPd1JEcid9YEi4F0ue6m1039EwR5top+xp
Date: Mon, 9 Jun 2014 10:13:29 +0000
Message-ID: <[email protected]>
References: <[email protected]>
In-Reply-To: <[email protected]>
Accept-Language: en-US
Content-Language: en-US
X-MS-Has-Attach:
X-MS-TNEF-Correlator:
x-originating-ip: [192.168.10.2]
Content-Type: multipart/alternative;
      boundary="_000_6b0d846f503942d99d44be9aff8d6adfogmaildomainnet_"
MIME-Version: 1.0
Queue viewer:
Identity: ogmail\8786\3470333575194
Subject: testing
Internet Message ID: <[email protected]>
From Address: [email protected]
Status: Active
Size (KB): 4
Message Source Name: SMTP:Default OGMAIL
Source IP: 192.168.10.12
SCL: -1
Date Received: 6/23/2014 3:22:49 PM
Expiration Time: 6/25/2014 3:22:49 PM
Last Error: 
Queue ID: ogmail\8786
Recipients:  [email protected];2;2;[{LRT=};{LED=};{FQDN=};{IP=}];0;CN=SendMail,CN=Connections,CN=Exchange Routing Group (DWBGZMFD01QNBJR),CN=Routing Groups,CN=Exchange Administrative Group (FYDIBOHF23SPDLT),CN=Administrative Groups,CN=First Organization,CN=Microsoft
Exchange,CN=Services,CN=Configuration,DC=domain,DC=net;0
Md. Ramin Hossain

Answer 1

What I notice is Queue expired. The message is not going out.
Failed to connect. Winsock error code: 10051, Win32 error code: 10051." Attempted failover to alternate host, but that did not succeed. Either there are no alternate hosts, or delivery failed to all alternate hosts.
This error states that It tried to connect to the target system but failed to connect out.
Is Exchange 2013 server added in the firewall rule to send communication over port 25?
Do you have use Front end proxy checkbox checked on the Send connector to internet that was created on 2013 (if created)?
If use front end proxy checkbox is checked, then you need to add permissions for your CAS server's IP in the Firewall for outbound port 25 rule. As it appears that the mail is originating from CAS to the firewall. If that checkbox is not checked, we need
to add the Mailbox server's IP on the outbound rule for port 25.