Learn English – her: a determiner or a pronoun

This is perhaps best explained by providing the relevant extract from the ‘Longman Student Grammar of Spoken and Written English’:

The double genitive is a special construction in which either the independent genitive or a possessive pronoun occurs in an of-phrase:

This was a good idea of Johnny’s.

There’s a talk by this lady from Boulder who’s a student of Sandy’s.

The woman who owns Harte’s is a friend of ours.

As these examples show, the main noun phrase typically begins with the indefinite article. In fact, the definite article does not normally combine with the double genitive: *the good idea of Johnny’s is unlikely to occur.

The meaning of the double genitive can sometimes be alternatively expressed by other constructions. Thus, a friend of ours could alternatively be expressed as one of our friends.

Here is a further explanation from ‘The Cambridge Guide to English Usage’:

The double genitive seems to serve two purposes:

emphasis. This is the effect of paraphrasing “not Jo’s fault" as no fault of Jo’s, or turning “our friend” into a friend of ours. The double genitive unpacks the phrase and foregrounds the noun rather than the person. In conversational examples such as That book of Bill Bryson’s is his best yet, the construction helps to adjust the topical focus.

clarification. Clearly a painting of Lady Rich’s and a painting of Lady Rich mean different things. The first (a possessive) makes the painting part of Lady Rich’s collection, while the second (technically an objective genitive) says that it is a portrait of the Lady herself. The duplication of the genitive is thus not redundant but clarifies the fact that the first construction is a possessive genitive.

This is part of a larger phenomenon than just this one pair of words in English. In German, we see the same coincidence with ihr, which is used for both third-person feminine dative pronoun and the third-person feminine possessive determiner. We also see the same forms used in German for the genitive and dative case of feminine singular nouns and articles, as in "der Hilfe" which can be genitive or dative.

It seems to be caused just by an accidental collision of originally distinct forms for feminine singular words. Sound changes eroded the ends of words in ways that caused these two different functions to be expressed by identical forms.

For the possessive pronouns his and her, Wiktionary gives the Proto-Germanic forms as *hes and *hezōz respectively.

The "objective" pronouns him and her are etymologically derived from dative-case forms, which Wiktionary gives as *himmai and *hezōi in Proto-Germanic.

You can see that at the Proto-Germanic stage, the ancestors of possessive and objective her are reconstructed as having distinct forms. Subsequent sound changes would explain why they fell together in modern English and German. Gothic apparently did not undergo sound changes like that.