Given a prime ideal $P$ in a valuation ring $A$, there is a valuation ring $B$ containing $A$ such that $B/PB$ is the fraction field of $A/P$ ?

Question

Let $(A,\mathfrak m)$ be a valuation ring (https://en.wikipedia.org/wiki/Valuation_ring ). Let $P$ be a prime ideal of $A$. I know that $A/P$ and $A_P$ are valuation rings .

How to show that there is a valuation ring $B$ , containing $A$, with maximal ideal $PB$ and such that $B/PB$ is the fraction field of $A/P$ ?