What is the best way to raise a mail server on Windows?

Question

Mail server

You need a mail server. We raised it based on hmailserver and got a full set of features. But hmailserver works well as an MDA (Mail Delivery Agent, Email Delivery Agent) and everything is fine with the POP3 and IMAP (imap4) protocols, incoming mail arrives, the smap filter works. But outgoing mail only works within the network. In the case of sending mail to other mail services (I tried Gmail, Yandex.Mail and Mayra), the mail leaves via SMTP, but does not reach the addressee. We checked the smap, inbox, and mailings, but there was no letter anywhere.
What solution do you recommend for Windows, so that SMTP works 100% (preferably POP3 with IMAP, so that everything can be transferred to one platform, but not necessarily)?! What Web mail do you recommend for this?! What are Web Admins?

Logs

* Обрабатывать POP перед SMTP...
* Учётная запись 'hMail': Соединение с POP3 сервером: trainzcity.myftp.org:995...
[2020-03-20 11:46:11] POP< +OK POP3
[2020-03-20 11:46:11] POP> USER [email protected]
[2020-03-20 11:46:11] POP< +OK Send your password
[2020-03-20 11:46:11] POP> PASS ********
[2020-03-20 11:46:11] POP< +OK Mailbox locked and ready
[2020-03-20 11:46:11] POP> QUIT
[2020-03-20 11:46:11] POP< +OK POP3 server saying goodbye...
* Учётная запись 'hMail': Соединение с SMTP сервером: trainzcity.myftp.org:587...
[2020-03-20 11:46:11] SMTP< 220 trainzcity.myftp.org ESMTP
[2020-03-20 11:46:11] ESMTP> EHLO localhost
[2020-03-20 11:46:11] ESMTP< 250-trainzcity.myftp.org
[2020-03-20 11:46:11] ESMTP< 250-SIZE 20480000
[2020-03-20 11:46:11] ESMTP< 250-STARTTLS
[2020-03-20 11:46:11] ESMTP< 250-AUTH LOGIN
[2020-03-20 11:46:11] ESMTP< 250 HELP
[2020-03-20 11:46:11] ESMTP> STARTTLS
[2020-03-20 11:46:11] ESMTP< 220 Ready to start TLS
[2020-03-20 11:46:11] ESMTP> EHLO localhost
[2020-03-20 11:46:11] ESMTP< 250-trainzcity.myftp.org
[2020-03-20 11:46:11] ESMTP< 250-SIZE 20480000
[2020-03-20 11:46:11] ESMTP< 250-AUTH LOGIN
[2020-03-20 11:46:11] ESMTP< 250 HELP
[2020-03-20 11:46:11] ESMTP> AUTH LOGIN
[2020-03-20 11:46:11] ESMTP< 334 VXNlcm5hbWU6
[2020-03-20 11:46:11] ESMTP> [USERID]
[2020-03-20 11:46:11] ESMTP< 334 UGFzc3dvcmQ6
[2020-03-20 11:46:11] ESMTP> [PASSWORD]
[2020-03-20 11:46:11] ESMTP< 235 authenticated.
[2020-03-20 11:46:11] ESMTP> MAIL FROM:<[email protected]> SIZE=400
[2020-03-20 11:46:11] SMTP< 250 OK
[2020-03-20 11:46:11] SMTP> RCPT TO:<[email protected]>
[2020-03-20 11:46:11] SMTP< 250 OK
[2020-03-20 11:46:11] SMTP> DATA
[2020-03-20 11:46:11] SMTP< 354 OK, send.
[2020-03-20 11:46:11] SMTP> . (EOM)
[2020-03-20 11:46:11] SMTP< 250 Queued (0.096 seconds)
* Почта отправлена успешно.
[2020-03-20 11:46:11] SMTP> QUIT
[2020-03-20 11:46:11] SMTP< 221 goodbye
* Обрабатывать POP перед SMTP...
* Учётная запись 'Rostik': Соединение с POP3 сервером: metrocraft.myvnc.com:995...
[2020-03-20 11:52:50] POP< +OK POP3
[2020-03-20 11:52:50] POP> USER [email protected]
[2020-03-20 11:52:50] POP< +OK Send your password
[2020-03-20 11:52:50] POP> PASS ********
[2020-03-20 11:52:50] POP< +OK Mailbox locked and ready
[2020-03-20 11:52:50] POP> QUIT
[2020-03-20 11:52:50] POP< +OK POP3 server saying goodbye...
* Учётная запись 'Rostik': Соединение с SMTP сервером: metrocraft.myvnc.com:465...
[2020-03-20 11:52:50] SMTP< 220 trainzcity.myftp.org ESMTP
[2020-03-20 11:52:50] ESMTP> EHLO trainzcity.myftp.org
[2020-03-20 11:52:50] ESMTP< 250-trainzcity.myftp.org
[2020-03-20 11:52:50] ESMTP< 250-SIZE 20480000
[2020-03-20 11:52:50] ESMTP< 250-AUTH LOGIN
[2020-03-20 11:52:50] ESMTP< 250 HELP
[2020-03-20 11:52:50] ESMTP> AUTH LOGIN
[2020-03-20 11:52:50] ESMTP< 334 VXNlcm5hbWU6
[2020-03-20 11:52:50] ESMTP> [USERID]
[2020-03-20 11:52:50] ESMTP< 334 UGFzc3dvcmQ6
[2020-03-20 11:52:50] ESMTP> [PASSWORD]
[2020-03-20 11:52:50] ESMTP< 235 authenticated.
[2020-03-20 11:52:50] ESMTP> MAIL FROM:<[email protected]> SIZE=458
[2020-03-20 11:52:50] SMTP< 250 OK
[2020-03-20 11:52:50] SMTP> RCPT TO:<[email protected]>
[2020-03-20 11:52:50] SMTP< 250 OK
[2020-03-20 11:52:50] SMTP> RCPT TO:<[email protected]>
[2020-03-20 11:52:50] SMTP< 250 OK
[2020-03-20 11:52:50] SMTP> RCPT TO:<[e-mail]>
[2020-03-20 11:52:50] SMTP< 250 OK
[2020-03-20 11:52:50] SMTP> DATA
[2020-03-20 11:52:50] SMTP< 354 OK, send.
[2020-03-20 11:52:50] SMTP> . (EOM)
[2020-03-20 11:52:51] SMTP< 250 Queued (0.140 seconds)
* Почта отправлена успешно.
[2020-03-20 11:52:51] SMTP> QUIT
[2020-03-20 11:52:51] SMTP< 221 goodbye
* Учётная запись 'Rostik': Соединение с SMTP сервером: metrocraft.myvnc.com:465...
[2020-03-20 11:53:50] SMTP< 220 trainzcity.myftp.org ESMTP
[2020-03-20 11:53:50] ESMTP> EHLO trainzcity.myftp.org
[2020-03-20 11:53:50] ESMTP< 250-trainzcity.myftp.org
[2020-03-20 11:53:50] ESMTP< 250-SIZE 20480000
[2020-03-20 11:53:50] ESMTP< 250-AUTH LOGIN
[2020-03-20 11:53:50] ESMTP< 250 HELP
[2020-03-20 11:53:50] ESMTP> AUTH LOGIN
[2020-03-20 11:53:50] ESMTP< 334 VXNlcm5hbWU6
[2020-03-20 11:53:50] ESMTP> [USERID]
[2020-03-20 11:53:50] ESMTP< 334 UGFzc3dvcmQ6
[2020-03-20 11:53:50] ESMTP> [PASSWORD]
[2020-03-20 11:53:50] ESMTP< 235 authenticated.
[2020-03-20 11:53:50] ESMTP> MAIL FROM:<[email protected]> SIZE=401
[2020-03-20 11:53:50] SMTP< 250 OK
[2020-03-20 11:53:50] SMTP> RCPT TO:<[email protected]>
[2020-03-20 11:53:50] SMTP< 250 OK
[2020-03-20 11:53:50] SMTP> DATA
[2020-03-20 11:53:50] SMTP< 354 OK, send.
[2020-03-20 11:53:50] SMTP> . (EOM)
[2020-03-20 11:53:50] SMTP< 250 Queued (0.064 seconds)
* Почта отправлена успешно.
[2020-03-20 11:53:50] SMTP> QUIT
[2020-03-20 11:53:50] SMTP< 221 goodbye

Answer 1

Check for delivery errors. In fact, the external server must return the message.
In addition, why are there no sessions on the external smtp, it looks like they are on the transit server and are dying