We derive an integral representation for the fundamental solution of the Kolmogorov forward equation: $$f_t = -((1 + \mu x) f)_x + (\nu x^2 f)_{xx}$$ associated with the Shiryaev process $X$ solving: $$dX_t = (1 + \mu X_t)\,dt + \sigma X_t\,dB_t$$ where $\mu \in \mathbb{R}$, $\nu=\sigma^2 /2>0$ and $B$ is a standard Brownian motion. The method of proof is based upon deriving and inverting a Laplace transform. Basic properties of $X$ needed in the proof are reviewed.