  A proper merging of two disjoint quasi-ordered sets $P$ and $Q$ is a
quasi-order on the union of $P$ and $Q$ such that the restriction to $P$ or $Q$
yields the original quasi-order again and such that no elements of $P$ and $Q$
are identified. In this article, we determine the number of proper mergings in
the case where $P$ is a star (i.e. an antichain with a smallest element
adjoined), and $Q$ is a chain. We show that the lattice of proper mergings of
an $m$-antichain and an $n$-chain, previously investigated by the author, is a
quotient lattice of the lattice of proper mergings of an $m$-star and an
$n$-chain, and we determine the number of proper mergings of an $m$-star and an
$n$-chain by counting the number of congruence classes and by determining their
cardinalities. Additionally, we compute the number of Galois connections
between certain modified Boolean lattices and chains.
