  We show that the set of increasing factorizations of fixed-point-free (FPF)
involution words has the structure of queer supercrystals. By exploiting the
algorithm of symplectic shifted Hecke insertion recently introduced by Marberg,
we establish the one-to-one correspondence between the set of increasing
factorizations of fixed-point-free involution words and the set of primed
tableau (semistandard marked shifted tableaux) and the latter admits the
structure of queer supercrystals. In order to establish the correspondence, we
prove that the Coxeter-Knuth related FPF-involution words have the same
insertion tableau in the symplectic shifted Hecke insertion, where the
insertion tableau is an increasing shifted tableau and the recording tableau is
a primed tableau.
