  We prove that for any $\mathbb{P}^n$-functor all the convolutions (double
cones) of the three-term complex $FHR \xrightarrow{\psi} FR \xrightarrow{tr}
Id$ defining its $\mathbb{P}$-twist are isomorphic. We also introduce a new
notion of a non-split $\mathbb{P}^n$-functor.
