How to open a remote connection to SMTP and IMAP?

Question

SMTP

Hello!
I have been studying mail servers for 2 days. It's already 6 o'clock today, I can't open remote access to SMTP and IMAP. I think the problem is in the IP.
For internal use, everything works, including sending emails to other servers (gmail, hotmail).
Bundle:
OS: Windows Server 2008 R2 (Azure VM)
Mail Server and Client, hosting, DB: hMailServer, Rouncube, IIS, MySQL Server
SMTP Server: localhost
IMAP server: Internal IP
PS All required ports are open.
PPS Changing IP Servers does not help, everything breaks.

Answer 1

telnet
telnet that's it, connect to the IMTP SMTP ports by telnet to that host. what you need, you see - what is open / closed
then connect with the application