Issue symptoms
When I open a messaging ticket, I cannot solve it. What is causing this behaviour?
Resolution steps
When a conversation is active, only the ticket assignee—the person who owns the conversation with the end user— can mark the ticket as Solved.
If you are not the Assignee of the ticket, you cannot change the status of an active messaging ticket to Solved.

For more information, see Why can't I set my ticket to solved.