Two servers one domain

[sgt_kovalsky]

Hello!
I have one server with the name mail.example-ep.com (11.111.1.111) with a mail domain (exsample-ep.com), which is spinning from the provider. There is a need to configure the second Zimbra with the same mail domain so that he uses the server provider as relay for sending and receiving letters. The second Zimbra has name zimbra.example.com which is spinning in my domain example.com and have the local address is 222.222.2.2.
In the web interface of second Zimbra i specified the name mai.example-ep.com for zembraMTaReLayNost, but he is sending letters by himself and not receiving anything.
Please tell me where to dig. I have read official guide for administrator and section about SplitDomain on wikiZimbra, but did not find that either useful for my case.
Thanks for all information!