Can the factory invoice the consulting service fee?

Of course. If there are no conditions for issuing invoices, you can go to the tax bureau to issue them. Invoicing is an obligation, not a right. If it only happens occasionally, you can directly issue relevant invoices. If this kind of business is expected to happen frequently in the future, the tax law stipulates that there is a tax obligation to issue invoices, and there is no restriction on enterprises to issue invoices. But in order to standardize the operation, this service can be added to the business scope.