$$\int_0^t {dt_1} \int_0^t {dt_2} \int_0^t {dt_3} B(t - t_3)F(t_3 - t_2)S(t - t_2)F(t_2 - t_1)F(t_1) \\
=\int_0^t {dt_2}\, (B*F)(t - t_2)S(t - t_2)(F*F)(t_2) \\ 
=((B*F)S)*(F*F))(t).$$