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Using a result of Koenig we show that if we have a $\\mathbb{D}^{{\\rm{b}}}({\\rm{{mod\\mbox{-}}}} )$ level recollement, writing $A$ in terms of $B$ and $C$, then we get a $\\mathbb{D}^-({\\rm{Mod\\mbox{-}}} )$ level recollement of certain functor categories, induces from the module categories of $A$, $B$ and $C$. As an application, we generalise the main theorem of Pan [Sh. Pan, Derived equivalences for Cohen-Macaulay Auslander algebras, J. Pure Appl. Algebra, 216 (2012), 355-363] in terms of recollements of Gorenstein artin algebras. 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