Julia sets converging to filled quadratic Julia sets

Previous results by Devaney et al. have shown that for the family of singularly perturbed quadratic maps $z^2 + \lambda/z^2$ the Julia sets converge to the unit disk as $\lambda \to 0$. We give a generalization of this result to maps of the family
$$ F_\lambda(z) = z^2 + c +\lambda/z^2 $$
where $c$ is the center of a hyperbolic component of the Mandelbrot set. Using symbolic dynamics and Cantor necklaces, we show that as $\lambda \to 0$, the Julia set of $F_\lambda$ converges to the filled Julia set of $z^2+c$.