Is this convolution product reversible?

Question

I am doing an exercise on Fourier transforms and i have the following questions which i really tried to solve myself

1. Let $k > 0$ and consider $F_k(x)$ a function with real values where $$F_k(x)=\begin{cases} 1/k & 0 \le x \le k \\0 & \text{otherwise}\end{cases}.$$ Compute The Fourier transform of $F_k$.

2. Considering a $[-\pi, \pi]$ band limited signal, is $u*F_k$ a reversible operation, where * is the convolution operator? If yes,justify you answer with $k$ values where this hypothesis is true.

Now it is easy to answer to question 1 where $F_k(f)=-(1+ e^{ikf})/ikf$ but the challenge is to answer question 2 using the one above. I tried to explicit the convolution product without any significant result. Any clues?