On uniqueness of P-twists

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