Let $\mfI$ be the class of fully zero-simple semihypergroups generated by a hyperproduct. In this paper we study some properties of residual semihypergroup $(H_+, \star)$ of a semihypergroup $(H,\circ)\in \mfI$. Moreover, we find sufficient conditions for $(H,\circ)$ and $(H_+, \star)$ to be cyclic.