outbound connector issue

Well to keep b, and remove a.
You need to do a process called "migration", so move all the mailboxes from the databases in 2003 and do the "moverequests" to change the mailboxes from 2003 to 2010.

When you have all the mailboxes in 2010, you need to do the Connectors to External (send connector) and the receive the default of exchange 2010 would work, work with the certificate to move it to 2010 if it's not there, set internal and external service entry points (scp), update firewall rules and internal and external dnss

Then you can remove the exchange server 2003 and of course, update the exchange 2010 to sp3.

Here's a guide: https://gallery.technet.microsoft.com/office/Rapid-Migration-Guide-from-7ade7012

Hi Jose thanks for the guide. As i go through i will need a few clarifications as i am not an expert in this field

I am using smart host with barracuda. is there any guide on this.
If you’re using smart hosts like barracuda, Change it in the (Smart host) barracuda settings. Any guide on this as i have not used barracuda before

Send connector was already there when i installed exchange on a and also on b. Do i need to create a new one?

Receive connector was already there as well do i need a new one?

I have already moved OAB and public folders without moving mailboxes will there be any problems?

How can i know if "Upgrading Email Address Policies and Address lists from Exchange 2003 to Exchange 2010" has already been done. i mean how can i confirm what do i have to look for

The 1st thing you need to do is to document your mailflow.
So, start by finding out how is the emails going out and in, how? https://mxtoolbox.com/EmailHeaders.aspx
getting the hops in the header of the incoming and outgoing message.
With this information you can know where are going he outgoing messages and thats the connectors you need to replicate in 2010 in case that you remove 2003 and the emails aren't going out.

Barracuda is a service for antispam, and no the send connectors aren't there because of act of magic, they aren't created when you do a clean install on a clean environment of exchange, the send connectors were Replicated from 2003 to 2010, in fact, if you install any version 2010,2013 or 2016 in a clean environment you won't get any send connector, this is the reason why you had a send connector.

Receive connectors are there in 2010 in 2003. So no, you don't need to create any.
If you are planning to do migrations your best bet is to get somebody that could do it for you because always there are many details to do a migration, especially if you're not an expert on the field.

No problems since you already moved the difficult part, now the mailboxes is easier, (also depends on their size, and network (speed of the movements).

For the email policies in 2010 you have a 2010 organization:
Organization Configuration > Hub Transport > you should have another tab called email policies, and that kind of things can't be migrated so you need to get all the configurations from 2003 and create a new policy in 2010, and then remove the 2003 policy.
https://technet.microsoft.com/en-us/library/bb125137(v=exchg.141).aspx

how can i ensure that port 25 is open - i did do netstat -an
protocol       local address    foreign address            state
tcp                 0.0.0.0:25           0.0.0.0                          listening
tcp                 [::]:25                   [::]:0                             listening

does the above mean port 25 is ok. tried telnet it didnt work

After restarting Microsoft exchange information store service i am able to send one email out. when i send after that it wouldn't go. Appreciate assistance

the is no other solution that suggests to get rid of the first exchange server which was done in my situation