  We develop the theory of projective endofunctors for modules of Khovanov
algebras $K$ of type B. In particular we compute the composition factors and
the graded layers of the image of a simple module under such a projective
functor. We then study variants of such functors for a subquotient
$e\tilde{K}e$. Via a comparison of two graded lifts of the Brauer algebra we
relate the Khovanov algebra to the Brauer algebra and use this to show that
projective functors describe translation functors on representations of the
orthosymplectic supergroup $\mathrm{OSp}(r|2n)$. As an application we get a
description of the Loewy layers of indecomposable summands in tensor powers of
the natural representation of $\mathrm{OSp}(r|2n)$.
