(This is only tangentially related to your post) I have no problem with policies against self-plagiarism because you shouldn't receive credit for 2 assignments when you only did half of the work. There are plenty of courses with overlapping content areas, so if they have open-ended types of assignments (write an essay or lit review on a relevant topic of choice), students shouldn't be able to just submit work from another class and then receive credit for both assignments/courses.
As some have pointed out, this is a somewhat unique circumstance in which it is the exact same class. Rather than the professor come to the student directly (which I don't really agree with because of the issues Mole raised- the universities ask instructors to submit instances of plagiarism through the formal process so there can be a proper record for each student's offenses), I think the student should have come to the professor. This has come up for me with students who failed my course and retook it. I've had a few students reach out proactively to discuss what I am comfortable with regarding their submitting previous work. My responses have been context-depedent. For the major assignments, I am fine with students using their past submissions as a reference or starting point, but it should be a unique work that is submitted. For more minor assignments that are application-based and personal (I teach mostly family, marriage, and sexuality courses), I ask them to consider their development and changing contexts in light of what they previously wrote and make any relevant changes.