  Let $k$ be a field of positive characteristic $p>2$. We prove a duality
property concerning the kernel of coinduced representations of Lie
superalgebras. This property was already proved by M. Duflo for Lie algebras in
any characteristic under more restrictive finiteness conditions. It was then
generalized to Lie superalgebras in characteristic 0 in previous works of the
author. In a second part of the article, we study the links between coinduced
representations and induced representations in the case of restricted Lie
superalgebras.
