Yes, they can! Seesaw supports a unified student journal across grade levels and school years with Seesaw for Schools.
In the free version of Seesaw, it's not possible to keep journals connected to student accounts when you move a student to a new class. Moving students from class to class (or year to year) is only possible with our paid school-wide service. Teachers and Admin can have access to previous year's journals using the Historical Data Access Tool.
For teachers using the free version of Seesaw, we recommend that the new teacher start fresh by adding students as new students in the new class or new year.