He has his father's stubbornness.
This expression describes someone having a feature (like eyes, nose, chin, etc.) that looks like their parent's. For example:
You have your mother's lips.
Don't you think she has your ears?
You can also use this for personality features that a child shares with a parent:
He has his father's stubbornness.
You usually don't use "___ has your ___" to talk about people who aren't related, even if they do look alike.
Someone who is "stubborn" won't change their mind. Once they've made a decision, they will continue with that decision even if you give them a lot of good reasons to change. Here's how you use the word "stubborn":
Don't be so stubborn!
Being "stubborn" is usually a bad quality.
You can talk about this quality with the word "stubbornness":