Hi.

By default, child tickets set the Parent ticket’s agent as a Watcher of the child ticket.

This is: They should be already receiving notifications for changes in the child tickets.

Regards,

This could be completed using API calls in a workflow that is triggered when the child ticket is closed. First you would need to send a call to get the parent ticket id and then a second call using that parent ticket id to add a note to the parent ticket.

I use a similar flow to add a note to the parent ticket when a task is completed on a child ticket. 

Hello! Good day. Thanks for reaching out to us on community.

Regarding your query, yes, this can be achieved via the Freshservice API by configuring automations through the Workflow Automator. You can set up a workflow that triggers when a child ticket is resolved, and then sends a note to the parent ticket, indicating the resolution.

Reference:     
https://api.freshservice.com/#view_a_ticket
/api/v2/tickets/kid]?include=related_tickets

Another possibility is leveraging the "Parent-Child Synchronization" app from the Freshservice marketplace, which can automatically sync details like notes or status changes between parent and child tickets. This would eliminate the need for agents to manually check child tickets while keeping the parent ticket updated in real-time. However, this app does not support customization based on statuses.