  Let $i$ be a reduced expression of the longest element in the Weyl group of
type $A$, which is adapted to a Dynkin quiver with a single sink. We present a
simple description of the crystal embedding of Young tableaux of arbitrary
shape into $i$-Lusztig data, which also gives an algorithm for the transition
matrix between Lusztig data associated to reduced expressions adapted to
quivers with a single sink.
