How to properly organize the work of internal mail in the office?

Question

Mail server

Hello.
There is such a legacy:
The organization has Exchange 2013 as an internal mail server, but it does not look outside.
In general, now there is a strange scheme there, there is an external mailer purchased from a third-party organization, MX is configured for it, then it forwards all letters to an internal address that a special sorter program on Exchange listens to and takes everything from this address, putting everything into the right folder that it listens to itself Exchange.
in general, the scheme is as follows:
External mailer => sorter => Exchange
The scheme is rather crooked and another problem is that this sorter sometimes crashes and mail stops going outside, which users do not immediately notice.
I want to refuse all intermediaries and immediately put Exchange out, but somewhere I heard out of the corner of my ear that it is not recommended to do this.
Advise what to read, according to which scheme is better to organize, which would be convenient and if the diagnosis of problems did not turn into hell.

Answer 1

there are logs for diagnosing problems - look, read, there is software , in extreme cases, you yourself can write
and generally study the www.danshin.ms blog from cover to cover, the man writes very competently on Microsoft products

Answer 2

There is nothing wrong with publishing port 25 on the edge router. (Microsoft previously offered the TMG product, now it has been deprecated on the Exchange blog on Technet, the developers themselves assure that the MS mail infrastructure is running Exchange 2013 and published without additional tools like TMG, by simple port forwarding, of course, I would not believe them, but I think it makes no sense to play it safe in your conditions.)
Roughly, the scheme is as follows:
1. Publish (do port forwarding) port 25 from a white IP to the internal IP address of Exchange 2013 on port 25. For the test, you can from your home machine "telnet myserver.ru 25"
2. For the provider that holds your DNS zone, change the MX record to your white IP (in step 1) (- here, of course, the VPS Linux + Postfix scheme is possible -> and only open port 25 for it - but you will already implement this when you work out this scheme)
3. In Exchange 2013 - add a domain to Accepted Domain, configure Email Address Policy for users
Of course, for all three points it does not hurt to read the theory, but in general I outlined the scheme for you. If you have any questions - ask, I will try to answer.