Hi,
The system is capable of doing this by itself. The background/primary server runs a process called the catalog_sync_daemon. This process will synchronize status and activities from service desk to service catalog. To configure it review the settings in options manager under Service Catalog. You need to provide a valid user/pass so it can log into service catalog to perform the necessary web service calls and you can also define which activities are synchronized to the service catalog notes. Keep in mind if the external system ticket is cleared from an incident/request which came from catalog that can cause the synchronization not to take place. Service Desk uses the external system ticket to store the relationship back to catalog.
Once you have options manager configured restart all service desk service. You can review the cacalog_sync log file on the background/primary server to see if there are any issues connecting to service catalog.
Hope this helps.