  It is shown that any handle-irreducible summand of every stable-ribbon
surface-link is a unique ribbon surface-link up to equivalences. This is a
generalization of a previously observed result for a stably trivial
surface-link. Two applications are given. One application is an observation
that a connected sum of two surface-links is a ribbon surface-link if and only
if both of the connected summands are ribbon surface-links. The other
application is an observation that any sphere-link consisting of trivial
components is a ribbon sphere-link.
