I'm not exactly sure as where to start.
We know that the Laplace transform of $h(t) =$ the Laplace transform of $(f * g) = F(s)G(s)$, where $h(t) = (f * g) = \int_{0}^t f(t-T)g(T)\,dT$.
Thus, I was thinking of finding the derivative of $h(t)$ using the fundamental theorem of calculus, and then $d/dt(f*g)=f(0)g(t)$ hence Laplace transform of $(f(0)g(t)) = ?$
But that doesn't make sense.
Any help will be greatly appreciated, thank you in advance.