To edit an invoice in the Admin Console, you must have access to the Customers section and have edit user rights. Those with read-only access to the Customers section will not have access to the edit option.
Find the invoice you want to edit and go to the Invoice Actions dropdown at the top right of the Invoice Details page. You will see the option to "Edit Invoice". This will take you to the edit page. The invoice will not be edited until you click "Save Changes" on the edit page.