  We consider the inhomogeneous biharmonic nonlinear Schr\"odinger equation $$
i u_t +\Delta^2 u+\lambda|x|^{-b}|u|^\alpha u = 0, $$ where $\lambda=\pm 1$ and
$\alpha$, $b>0$. In the subctritical case, we improve the global well-posedness
result obtained in \cite{GUZPAS} for dimensions $N=5,6,7$ in the Sobolev space
$H^2(\mathbb{R}^N)$. The fundamental tools to establish our results are the
standard Strichartz estimates related to the linear problem and the
Hardy-Littlewood inequality. Results concerning the energy-critical case, that
is, $\alpha=\frac{8-2b}{N-4}$ are also reported. More precisely, we show
well-posedness and a stability result with initial data in the critical space
$\dot{H}^2$.
