Extension of $\mathrm{CR}$ functions into a wedge from a manifold of finite type

It is shown that, if a generating manifold $M\in C^n$ does not contain proper submanifolds of the same $\mathrm{CR}$ dimension as $M$, then all $\mathrm{CR}$ functions can be extended from $M$ into some wedge with edge $M$. In particular, extension of all $\mathrm{CR}$ functions into a wedge necessarily obtains for manifolds of finite type.
Bibliography: 21 titles.