This involves service invention. If the teacher made the invention in order to complete his own work or mainly by using the information of the company's funds, equipment and materials, then the invention originally belongs to the company, and the teacher can only ask for a certain reward, but can't obtain the patent right. If it is not a service invention, the applicant is a school at the time of application, that is to say, the right holder is still a school, not a teacher. In other words, there is a dispute over the ownership of rights between teachers and schools, which needs to be resolved through litigation before the patent right can be transferred to the teacher's name.
If we don't change the status quo, the patent right still belongs to the school, then teachers only have the right to sign patents, and teachers can't directly cooperate with enterprises. At most, he can only be a middleman to introduce the enterprise to the school. If the cooperation between them is successful, he can ask the school for some remuneration. Of course, this is not the scope of legal issues.