A is a Noetherian ring, B is an f.g. algebra over A, I is an ideal of A. let $\hat B$ be B's I-adic completion. Prove that $\Omega^1_{\hat B/A}$'s I-adic completion is isomorphic to $\Omega^1_{B/A}$'s I-adic completion.

This is an exercise from Liu's "Algebraic geometry and arithmetic curves", Exercise VI.1.3. It seems strange because according to Part(a) of that problem, there is an exact sequence involving these two objects. And if this is true, we must prove the first term in that exact sequence is actually zero under only Noetherian condition! I feel a bit puzzled, can anyone help me? Thanks!