А как тогда понимать это: (She should). Пример: He said that she should have the books in a few days.

Вот так это понимать, читайте:
http://idioms.thefreedictionary.com/supposed+to+do

И еще

(be supposed to do something) Be required to do something because of the position one is in or an agreement one has made:
I’m supposed to be meeting someone at the airport
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I thought these sessions were supposed to have a positive effect, if anything.
Shawn pulled up to the abandoned building where the gang meeting was supposed to be.
The consulting contract is supposed to reflect a meeting of the minds between the parties.
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AMERICAN ANAL SLUT - Переведите это предложение..

😂