You can enable this feature here:
WP-Admin > Awedesk > Configuration > Advanced > On Behalf.

This allows admins, managers, or agents, to create tickets on behalf of the clients.

How to create such a ticket is described here:
https://awedesk.com/documentation/frontend-agent/creating-a-ticket-on-behalf-of-the-client/

If the client is not found in the database (choosing the client’s name from the list is not possible), you can create new a client when submitting a ticket.

You can choose one of the below role options: