Triviality of the second cohomology group of the conformal algebras $\mathrm{Cend}_n$ and $\mathrm{Cur}_n$

It is proved that the second cohomology group of the conformal algebras $\mathrm{Cend}_n$ and $\mathrm{Cur}_n$ with coefficients in any bimodule is trivial. As a result, these algebras are segregated in any extension with a nilpotent kernel.