I think that this is an example of deviation from the "predicate-subject-object rule" on Gramadach na Gaeilge : if you understand German, have a look at "Identifikationssätze mit Eigennamen, Demonstrativpronomen und Substantiven mit Demonstrativpronomen" in there. The outdated English version doesn't have this paragraph unfortunately
This exercise is analogous to the Is é an fear sin an dalta. = Jener Mann (Subjekt) ist der Schüler (Prädikat). example on the braesicke.de page, which matches the “with a definite noun as the subject after the predicate” section on __ — a noun that follows a possessive adjective is also a definite noun.
Heads-up : I edited this several times already, and I'll edit it again when everything becomes clear.
Wait ! :) Sorry, but I don't think so ; at least, both might be possible (see below the translation of the paragraph I was referring to). It's not yet completely clear for me, but I think I'm going to ask the author, as I've already been in contact with him. As you noted yourself, it is analogous to Is é an fear sin an dalta. = Jener Mann (Subjekt) ist der Schüler (Prädikat). = That man (subject) is the student (predicate). So, we indeed get That man is her teacher., and not Her teacher is that man. And the part you provided a link to is the situation without a demonstrative pronoun, outside of those "exceptions to the PSO rule" section.
Here's my translation for the paragraph I was referring to. I cannot guarantee 100 % accuracy as I'm not a native German speaker, but hopefully it will help :
Identificatory sentences with proper nouns, demonstrative pronouns and substantives with demonstrative pronouns
Proper names, demonstrative pronouns and substantives with demonstrative pronouns usually (that is, in sentences expressing a neutral statement) come first; when they are subject, they are therefore before the actual predicate. However, they are still separated from the copula by a subpredicate (é/í/iad), so that, from a formal point of view, the PSO-rule holds. For example:
Is é Pól an múinteoir. = Paul (subject) is the teacher (predicate).
Is é an fear sin an dalta. = That man (subject) is the student (predicate).
Is é sin an dalta. = That (one) (subject) is the student (predicate).
With demonstrative pronouns, an abbreviated form is also common, in which the demonstrative pronoun is regarded as a combination with the copula and stands directly at the beginning of the sentence (in the Standard, only in the non-dependent present tense). In this case, the subpredicate follows the demonstrative pronoun; as a consequence, the PSO rule does not hold anymore. For example:
Sin é an dalta. = That is the student.
Sentences with proper names, demonstrative pronouns or pronouns of the 1st or 2nd person as subjects at the end of a sentence are rare and unusual, but not entirely impossible: Is é an múinteoir Pól; Is é an dalta an fear sin; Is é an dalta é sin; Is é an dalta mé. They are used only when the predicate should be particularly emphasised (as extraordinary, remarkable, etc.), corresponding to the common stress on the article in German: e.g.: Is é an múinteoir Pól. = Pól is the (famous, high-profile, extraordinary) teacher.
Looking at the braesicke.de “syntax of the copula” page, the usage description is more thorough for when the subject precedes the predicate, and includes situations that aren’t on its GnaG analogue. One of those situations is when the subject has a demonstrative, e.g. Is é an sagart sin an t-easpag. = Jener Priester ist der Bischof. = “That priest is the bishop.”, so your original point is correct, as is the translation for the exercise.
Those of us who depend on GnaG should also brush up on German and check braesicke.de for “updates”!
Wow so for those of us who have no idea what any of you just said and don't speak German. How does one determine that the man is her teacher. Rather than his teacher or just a teacher. Please don't use the fancy language major speak that won't help me. Just down and dirty ie this letter or word means this next word is this sex
Is é an fear sin a múinteoir - "that man is her teacher"
Is é an fear sin a mhúinteoir - "that man is his teacher"
The difference between a múinteoir/"her teacher" and a mhúinteoir/"his teacher" is the séimhiú in mhúinteoir. These are identification sentences.
Is múinteoir é an fear sin - "that man is a teacher".
This is a classification sentence.