If A and B are finite dimensional k-algebras, k is a field. $_{A}G\in A-mod$ is a Gorenstein projective module, then we have $RHom_{A}(G,A)\simeq Hom(G,A)$ since $Ext_{A}^{i}(G,A)=0$ for any $i\in \mathbb{Z}^{+}$. It is easy to prove that for $P\in K^{b}(A-proj)$ we have $RHom(G,P)\simeq Hom(G,P)$ in $D(k)$. If $_{A}X_{B}$ is a bi-module complex and $_{A}X\in K^{b}(A-proj)$, we know $RHom_{A}(G,X)\simeq Hom(G,X)$ in $D(k)$. My question is if $RHom_{A}(G,X)\simeq Hom(G,X)$ in $D(B^{op})$?