Convergence of distributions and Principal Value

Question

I'm doing an exercise on Fourier Transforms that has several sections. In the first one I've managed to prove $f_n(x)=\frac{1}{(x+i/n)}\in\mathcal{S'(\mathbb R)}$ and I've calculated $\mathcal{F}(f_n)(\omega)=-2\pi i e^{\frac{-2\pi \omega}{n}}H(\omega)$. In the second section I've proved that $\{\mathcal{F}(f_n)\}_{n=1}^{\infty}$ converges to $-2\pi iH$ in $\mathcal{S'}(\mathbb R)$. But now I have to deduce that $\{f_n\}_{n=1}^{\infty}$ converges to $P.V.(\frac{1}{x})-i\pi\delta$ in $\mathcal{S}(\mathbb R)$ and I don't know how to do this. I need some help. Thanks!