In the first sentence, "another" is the only correct option. In the second, either word may be used correctly. I personally would say in the second sentence, “If a school closure or other situation is preventing . . .." It sounds more "natural" to me.

Fernando, In the first sentence, the second direct object, “submenu” is a countable noun that represents no specific thing, so it needs an indefinite article (a or an). Because it is modified essentially by the adjective “other,” which begins with a vowel sound, it needs the indefinite article “an,” and the “an” is supplied within the word “another.” The bare “other” supplies no “an,” so it is not acceptable. The big difference between the two sentences is that in the first, there is no indefinite article prior to the one that “submenu” requires, but in the second, there is. In the second sentence, “another” will fit in nicely before “situation, but it’s not the only option. A discussion of what I am talking about is found in Follett, Wilson, et al. Modern American Usage: a Guide. Hill & Wang, 1966., page 353.” There the authors talk about words that are left out of sentences but are nonetheless “understood” to be there. For instance, “We ought to say, an awkward and a stupid man, but we often say an awkward and stupid man” (Follet et al. 353). Such departures from strict adherence to grammar are tolerable, they say, especially when the indefinite article preceding a previous noun is incorrect for the subsequent noun phrase in the sequence. So for the second sentence, rather than prescribing that “another” must be used in order to put an “an” before the second noun, the authors consider it permissible to “ride on the coattails,” as it were [my idiom, not theirs], of the previous indefinite article, even though it is the wrong indefinite article for the second noun phrase, i.e., “other situation” here. I was remiss. As a learner of English as a Second Language, you should use only “another” in both sentences. That way, prescriptive grammarians will accept your efforts. Be aware, however, that effective writers of English do not always comply with every technical rule of grammar when the resultant sentence will not be open to misconstruction by the reader.

“Then you have to select Advanced Options or another submenu to find it.” “If a school closure or another situation is preventing your child from being fed, please count on us”

another (: