We show that two Alexander biquandles M and M' are isomorphic if and only if there is an isomorphism of Z[s(+1), t(+1)]-modules h : (1 - st)M -> (1 - st)M' and a bijection g : O-s(A) -> O-s(A') between the s-orbits of sets of coset representatives of M/(1- st) M and M'/(1 - st)M' respectively satisfying certain compatibility conditions.