I'm having trouble figuring this out, but I'm pretty sure it is only a few lines for someone who understands this a little better:

"Suppose that T_1 is sufficient and T_2 is minimal sufficient. Let U be an unbiased estimator of \theta and define  U_1 = E(U|T_1) and U_2 = E(U|T_2). Show that U_2 = E(U_1|T_2)."