We have 2 diferents domains subscription into Office 365 ( teacher.domain.com and student.domain.com) , how can make to connect/share users from student.domain.com to teacher.domain.com?. This because we need to add that users to Lists, Groups, Classroom, or Sharepoint apps.
Do you have two separate Office 365 tenants? You can have multiple domains in an Office 365 tenant. Example: You sign up for a new Office 365 tenant and you get school.onmicrosoft.com and add your custom domain (school.com). Now you will have two domains, the default school.onmicrosoft.com and school.com. Yes, you can add your subdomains as well. students.school.com and teachers.school.com. When you look at the Domains screen you will see them all. As you provision users, you will have the option to select the domain for that user.
Now, if you do have separate tenants, as far as I know now, you cannot have a two-way trust with different Office 365 tenants. You can migrate one tenant to the other.
If you need to keep the Office 365 tenants separate you set up sharing from the services to the other users.