While connecting multiple email accounts to the iPhone devices, the Calendar invitation received via Mail app and external IMAP account is not synced to the Kerio Connect server. The Calendar event is being processed as a .ics file in the Apple Mail application.
The Kerio Connect account is configured using the Exchange ActiveSync (EAS) protocol. The IMAP account is set through external email provider.
The above procedure will not add the event to the ActiveSync calendar as desired and no request/response between iPhone Mail/Calendar App and Kerio using ActiveSync could be observed during those steps.
If the Calendar event is being added to Apple Calendar using Siri, the event is being displayed twice, but as the second invite (.ics attachment) is just a reference to the INBOX email, it will not be synced to Kerio Connect server.
This is clearly an iPhone Mail App behavior and not the Kerio Connect issue. For more information, please refer to the 3-rd party Apple discussion for iCloud ics invitations sent to Exchange on iPhone won't sync.
The issue is not presented when using the IMAP/CalDAV account instead of the Exchange Activesync profile. For more information about configuration, please refer to Integrating IMAP/CalDAV/CardDAV Accounts with Kerio Connect on iOS Devices.