In this paper we obtain the jump (or Rankine-Hugoniot) condition at the interphase for
solutions in the sense of distributions to the one phase Stefan problem $u_t= \Delta (u-1)_+.$ We do this by approximating
the free boundary with level sets, and using methods from the theory of bounded variation functions. We show that the spatial
component of the normal derivative of the solution has a trace at the free boundary that is picked up in a natural sense. The jump condition is then
obtained from the equality of the $n$-density of two different disintegrations of the free boundary measure. This is done under
an additional condition on the $n$-density of this measure. In the last section we show that this condition is optimal,
in the sense that its satisfaction depends on the geometry of the initial data.