I would suggest you add a <a href=”http://technet.microsoft.com/en-us/library/aa996980(EXCHG.65).aspx”>front end server</a> to your configuration.
Thank you for your answer! Sorry for my late reply but I was in vacation.
Regarding this proposal, it is a good idea, but I succeed to find in Internet another solution, which looks for me more easier to deploy:
1. Create a SMTP routing connector which has as smarthost the External SMTP connector.
2. This SMTP routing connector has both servers Exch1 and Exch2 as bridgeheads.
3. In Exch1 server the Smarthost should be removed from the original setting in Default SMTP Virtual Server.
In this way the communication works between Exch1 and Exch2 and to and from outside.
Here is the link: