Question: Upon answering the telephone, the person calling asks if Joan is available. If Joan is the person who answered the phone, should she say "This is her" or "This is she"? 
Answer: It's correct either way. English has lost its case system almost completely. This makes it hard even for native speakers to decide between subject case (nominative) and object case (formerly accusative/dative). A long time ago far too long ago to be directly relevant today , English still had a 'proper' case system and the copula be was followed by subject case. This is normal for Indo-European languages. Therefore, originally it would have been something like (translating to modern) "It is she". However, just like French but under the radar, English developed emphatic forms of its pronouns. When an adult asks a bunch of children "Qui veut de la glace ?" / "Who wants some ice cream?", the children's natural response is "Moi ! Moi ! Moi !" / "Me! Me! Me!", not "Je ! Je ! Je !" / "I! I! I!" This doesn't mean that the response is in dative / object case but that the response is emphatic. The same emphatic form of the personal pronoun is also used in connection with the copula etre / be: "C'est moi." / "This is me." The French third person feminine pronoun happens to have no special emphatic form. It's elle whether emphatic or not. In English, the non-emphatic subject case is she, and all other forms (object case and emphatic form) are her. Therefore, in natural English the correct answer is "This is her." This is how non-native speakers learn to say the sentence. For some reason, there is a tradition in English grammar (as taught to native speakers) to completely ignore the issue of emphatic pronouns and to assume that English has to work like German, which does not have them, or like Latin, where only emphatic pronouns exist and these carry the case distinctions. A non-native speaker who missed the drills for the emphatic pronouns but who, coming from another Indo-European language, knows about subject case after be, will quite logically say "This is she." English prescriptivism, in its trademark cluelessness (often pointed out by proper linguists), stepped into the same trap. English has a tradition of rules being made up by ignorant prescriptivists and then taught to generations of students and used as shibboleths that serve to distinguish those who received a 'proper' education from those who just use the language naturally and correctly, such as intelligent members of the working class and of course the likes of Charles Dickens and Jane Austen. As a result, "This is she" became a correct alternative again, long after it had fallen out of use. (Note on case terminology: English still has subject case and object case, though it only marks them on pronouns. It also has genitive pronouns, but since the former genitive suffix 's is now a possession-marking clitic, the status of genitive as a case in English is even less clear. English subject case is exactly the same thing that is called nominative in German, Latin etc. English object case is the result of a merger of accusative and dative, also known as accudative. This merger has long been completed in English, has almost completed in Dutch and many German dialects, but is still in progress in standard German.).
Output: no