Help with difference between べき and もの

Is using もの=should in the context of this sentence grammatically correct? If so what’s the difference in meaning? Both are used to express things you should do. I’ve read in A Dictionary of Intermediate Japanes Grammar p14 that べき is for a specific admonition to a particular person & that もの is used for general admonitions that reinforce societal norms. However, I get these 2 grammars mixed up and marked wrong in the quizzes & would like some help in distinguishing which one I should use.

edit: fixed typo

(I think you made a small typo and the sentence should use 知っておく and not しておく)

To answer the question, if the translation is meant to be something like “There is a lot of information in this book that people learning Japanese ought to know” or “In this book there is a lot of information that people learning Japanese should know” (or whatever your preferred English sentence is) then the answer is べき。

Basically, べき is for something that ought to happen. もの is for something that happens as a general fact (and therefore it “should” be that way insofar as it generally is that way). You could more directly translate sentences that use もの as “It is a thing that なになに”. E.g., (using the first Bunpro sentence for this) ケーキはあまものだ。 could be taken to mean "It is a thing that cake is sweet (so this cake, that we are talking about, should be sweet as well [and I probably am drawing attention to this fact because this cake isn’t sweet]). Cake being sweet is a fact; it is a thing; you can’t argue with it because that is just a thing that is like that, generally speaking. In context this usage is far far more obvious and the non-contextual nature of Bunpro sentences obscures this a bit.

For べき, the usage is more that something ought to be done, that there is no other way to go about doing the thing than that specific way. It is because of this that it can take on a less general tone. The usage is also less contrastative as it isn’t a statement about what is generally the case (“The thing of”) but rather the only way to go about something. Again, in context this is also way more obvious.

Regarding getting the answer on Bunpro: べき can only come after a verb. Some of the sentences are perhaps ambiguous when it is after a verb but that is a big hint.

Regarding the example sentence you gave: The book has information that someone studying Japanese “ought to know”. It doesn’t have information that someone studying Japanese “is supposed to know because in general if you study Japanese then you would know it - they are supposed to know it and that is just how it is”. Or, at least, one assumes this as the former makes more sense than the latter. Another hint, which you are not to have known, is that 知っておくべき is a not entirely uncommon collocation.

This is my understanding of it (although I don’t think I have explained it that well compared to many resources).