Third person singular possessive pronouns, the fancy name for his and her, pose a tricky problem for many languages. The crux is that both the possessors, i.e. he and she, and the nouns themselves have genders in most Western languages. When the owner and noun are the identical sex, everything is fine. The issue is when they are different.
For a change, English simplifies the issue. Nouns have no gender, unless they are biologically male or female, which does not affect the grammar. Therefore, his belongs to John and her belongs to Jane. Russian does have grammatical gender, but it doesn’t affect the pronoun in this case. Его [yevo] and ее [yeyo] are the Russian equivalents of Ivan's and Natasha's.
Hebrew takes the same route as Russian, i.e. one form for his and her regardless of gender, but often doubles the possessive: אישתו של יוסי. This comes out as his wife of Yosi, in case you didn’t figure out that she is married to Yosi. The most ambiguous, as usual, is French. The masculine son and feminine sa refer to the gender of the noun, not the owners. Son livre could belong to Jean or Jeanne. If you have to make it clear, you need to say Son livre à elle to ensure that everybody understands Jeanne went to the bookstore.
Unless you live in a kibbutz where mine is mine and yours is mine, it is always reassuring to know what is his and what is hers.