  For a scheme X, denote by SH(X_et^hyp) the stabilization of the
hypercompletion of its etale infty-topos, and by SH_et(X) the localization of
the stable motivic homotopy category SH(X) at the (desuspensions of) etale
hypercovers. For a stable infty-category C, write C_p^comp for the p-completion
of C. We prove that under suitable finiteness hypotheses, and assuming that p
is invertible on X, the canonical functor e_p^comp: SH(X_et^hyp)_p^comp ->
SH_et(X)_p^comp is an equivalence of infty-categories. The primary novelty of
our argument is that we use the pro-etale topology to construct directly an
invertible object Sptw[1] in SH(X_et^hyp)_p^comp with the property that
e_p^comp(Sptw[1]) = Sigma^infty Gm.
