Configure it under Settings → Security → Certificates (ACME), or in hMailServer.INI:

AcmeEnabled=1
AcmeContactEmail=you@yourcompany.com
AcmeDomains=mail.yourcompany.com,mta-sts.yourcompany.com,autoconfig.yourcompany.com
AcmeHttpPort=80
AcmeReuseKey=1

AcmeEnabled ships as 0. AcmeDirectoryUrl defaults to https://acme-v02.api.letsencrypt.org/directory.

Two requirements. Port 80 must be reachable from the internet, because that is how the http-01 challenge proves you control the name. Every name in AcmeDomains must already resolve to this server before you switch it on. If you also host MTA-STS or client autoconfiguration, put mta-sts.<domain>, autoconfig.<domain> and autodiscover.<domain> in AcmeDomains so one certificate covers them.

After issuance. The server creates or updates a certificate record named ACME (automatic) and assigns it to every TLS-enabled listener that has none of its own, logging each assignment. A listener the assignment could not be saved for is reported as a High 6100 rather than logged as a success, because a port left without a certificate accepts no TLS at all. That is the error to alert on.

Renewal. The renewal window is two thirds of the certificate lifetime, plus ARI. That is why there is nothing left to schedule. Files live in Data\ACME on Windows and /var/lib/hmailserver/ACME/ on Linux: the account key, fullchain.pem and privkey.pem. Back that directory up with the rest of Data\. If a restore misses it the client re-issues, but the new key invalidates any TLSA records you have published.

Leave AcmeReuseKey=1. Keeping the same private key across renewals is what keeps published TLSA records valid.

Linux. Port 80 works without root. CAP_NET_BIND_SERVICE on the unit is what allows the bind. The default certificate directory is <DataFolder>/ACME, which is inside ReadWritePaths. Point AcmeCertificateDirectory elsewhere and you must add that path to ReadWritePaths with a drop-in, or issuance fails on a read-only filesystem.

If it never worked for you. The built-in client had never once succeeded against real Let's Encrypt until 6.2.24 (#34). Boulder pretty-prints its JSON and the challenge locator searched for the compact spelling. 6.2.25 then fixed issuance and renewal ending the process (#93). If you gave up on this on an older build, it is worth another look.

Another CA. Leave AcmeEnabled=0, add the PEM certificate and key under Settings → Security → SSL certificates, then assign it to ports under Settings → Network → TCP/IP ports. On Linux, an external client that replaces the PEM files in place needs POST /api/v1/server/reinitialize or a restart before the new files are served.

Chapter 9, encryption and certificates: https://www.progressiverobot.com/hmailserver-documentation/#9-encryption-and-certificates
Report problems: https://gitlab.com/Progressiverobot/hmailserver