  The Minkowski background intrinsic to the Kerr-Schild version of the Kerr
metric provides a definition of a boosted spinning black hole. There are two
Kerr-Schild versions corresponding to ingoing or outgoing principal null
directions. The two corresponding Minkowski backgrounds and their associated
boosts differ drastically. This has an important implication for the
gravitational memory effect. A prior analysis of the transition of a
non-spinning Schwarzschild black hole to a boosted state showed that the memory
effect in the nonlinear regime agrees with the linearised result based upon the
retarded Green function only if the final velocity corresponds to a boost
symmetry of the ingoing Minkowski background. A boost with respect to the
outgoing Minkowski background is inconsistent with the absence of ingoing
radiation from past null infinity. We show that this results extends to the
transition of a Kerr black hole to a boosted state and apply it to set upper
and lower bounds for the boost memory effect resulting from the collision of
two spinning black holes.
