It’s true that توكيد must follow المؤكَّد, the exception is when you want to emphasize ضمير متصل, in this case you must use ضمير الرفع المنفصل whether alone or with the words نفسه وعينه.What would هو be in this sentence? Would it be a تأكيد of the pronoun ه in مدرسته? I don't think that's possible because the تأكيد is one of the five توابع, and the rule is that the تابع and متبوع are in the same case, i.e. they're both مرفوع or both منصوب or both مجرور. Here, ه is مجرور because it's the مضاف إليه, while هو is, of course, مرفوع. So, it can't be a تأكيد.