No, that would be sig, the reflexive pronoun. Like sie spiegelt sich = hon speglar sig = 'she sees/looks at herself in a/the mirror'.
(also German sich can mean 'each other' but Swedish sig cannot: sie lieben sich = de älskar varandra = 'they love each other')
German doesn't have a reflexive possessive pronoun like sin so Hon visar sin bok is Sie zeigt ihr Buch even if it's her own book. And Han visar sin bok is Er zeigt sein Buch = 'He shows his book', so German is more like English here.
Sin refers back to the subject - and the subject is the girl in this case. That's the whole purpose of the possessive reflexive pronoun - to avoid the ambiguity.
Flickan visar sin bok. --- The girl shows her (own) book.
Flickan visar hennes bok. --- The girl shows her (some other female's) book.
Flickan visar hans bok. --- The girl shows his (some male's) book.
Pojken visar sin bok. --- The boy shows his (own) book.
Pojken visar hennes bok. --- The boy shows her (some female's) book.
Pojken visar hans bok. --- The boy shows his (some other male's) book.
Can you use "hennes" in a sentence instead of "sin" anyway? Perhaps it's because at the time I didn't understand everything that was being said, but I remember my partner talking about my brother and saying "hennes bror blah blah blah".
I could be likely that I wasn't the focus of the subject so "hennes" was used but do native speakers sometimes just say hennes instead of sin or is that a childish way of speaking? I know there's lazy ways of speaking in english that arent inherently incorrect but don't sound right to listen to.