You want to create a Zendesk support ticket on behalf of another user.
If you have an End User-type account in Zendesk, you will not be able to create a ticket on behalf of other users. However, an agent can change the requester field on the ticket to a particular account.
As a workaround, you can create a new ticket with the actual request/issue that the user has and ask the agent to change the requester to the desired account. Keep in mind that the public messages you input in the ticket will also be visible to the other users.
Alternatively, you can ask the user to create a support ticket themselves.
<supportagent>You can share a list of the tickets already created by the customer to avoid ticket duplication.</supportagent>