To assign a chat to another agent, you need to click on Conversation actions in the third pane. Where you will be able to see Assigned agent field with the agent name to whom the chat is assigned.

Click on the agent name and you will be able to see the list of agents from which you can search and assign the chat to a particular agent.

Ex: If an agent is assigned to a chat but does not have the expertise to resolve it, then the agent can assign the chat to another agent who has knowledge of the issue.

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