Every message broadcast from Nexus Transmit includes the Client Identifying Information. If the client was added to Nexus through Nexus Sync and the Integration ID was supplied, then that will be the Integration ID included from Nexus Transmit. This should be how the client is uniquely identified in the Case Management System.
If an Integration ID has not been set for the client, then Nexus will use its own unique identifier as the Integration ID for messages sent through Nexus Transmit. The nexus generated unique identifier can be overwritten through Nexus Sync. This allows a client to be originally created in Nexus to then also be created in the Case Management System and the new identifier from CMS to be set as the Integration ID for the client.