Hi Miroslav,
If you want to keep AD Connect in place there is currently a recommendation (restriction) from Microsoft to retain an Exchange server on-prem to perform recipient admin tasks such as adding/amending email addresses etc. You can do this using ADSI edit but using an Exchange server is the only supported method. It is worth noting that this is a limitation of AD Connect (and not Exchange), as user accounts and mail-enabled objects are sync'd from the AD environment we will need to perform any email related tasks on the local object and allow the attributes to synchronise to O365. Often we deploy Exchange 2016 servers to act as management servers (sometimes referred to as hybrid servers) with no clients connections and no end user mail flow (although often used for SMTP relays as well).
I'd suggest taking a look at these articles which go into far more detail:
https://www.enowsoftware.com/solutions-engine/decommissioning-your-last-exchange-serverhttps://docs.microsoft.com/en-us/exchange/decommission-on-premises-exchangeI would add that many of us are waiting with baited breath for some developments in this area to allow us to remove that final Exchange server from our AD environment!
