How would you know that it's "her coat" as opposed to "his coat"?
There is no way to know without context, it could be either.
But aren't we need to conjugate the person of a noun ??? Or I misunderstood the rule about conjugation ??
Yes, but you put the gender depending on the thing "owned" (object) not on the subject.
la suA borsa ( borsa fem) (his/her bag)
il suO cappotto (cappotto masc) (his/her coat)