Minimal order semihypergroups of type U on the right, II

We prove a new characterization of the heart WH and of the derived DH of a finite semihypergroup H of type U on the right, in terms of its hyperproducts. Consequently, we characterize the minimal size of the proper semihypergroups H of type U on the right such that WH=DH≠H, WH≠DH≠H, or WH≠DH=H. Moreover, we obtain new results on the fundamental relations β and γ on finite semihypergroups of type U on the right. In particular, we prove that γ is transitive, β is transitive if |H|⩽8, and that there exist semihypergroups of type U on the right of size ⩾9 where β is not transitive. Hence, the minimal size for a semihypergroup of type U on the right to have a nontransitive β is 9.