  We formulate and prove the stability statement associated with the spacetime
Penrose inequality for $n$-dimensional spherically symmetric, asymptotically
flat initial data satisfying the dominant energy condition. We assume that the
ADM mass is close to the half area radius of the outermost apparent horizon
and, following the generalized Jang equation approach, show that the initial
data must arise from an isometric embedding into a static spacetime close to to
the exterior region of a Schwarzschild spacetime in the following sense.
Namely, the time slice is close to the Schwarzschild time slice in the volume
preserving intrinsic flat distance, the static potentials are close in
$L_{loc}^2$, and the initial data extrinsic curvature is close to the second
fundamental form of the embedding in $L^2$.
