Let f,g∈C1(R) and H be the Heaviside function. Consider the scalar conservation law ut​+F(x,u)=0, u(x,0)=u0​(x) for x∈R, t>0 and F(x,u)=H(x)f(u)+(1−H(x))g(u). Since the flux F is discontinuous at x=0, the general method of Kruskov is not applicable in order to obtain a solution. Using the Hamilton-Jacobi theory we obtain a unique solution satisfying the interphase entropy condition at the interphace x=0.