Positive Block Matrices

‎Let $C$ and $D$ be positive operators such that $C\\leq D$ and $D$ be invertible‎. ‎We show that there exists a trace preserving unital completely positive map $\\Phi_{C,D}:\\mathbb{B}(\\mathcal{H})\\rightarrow \\mathbb{B}(\\mathcal{H})$ such that ‎the ‎block ‎operator ‎matrices ‎\\begin{equation*}‎ ‎\\left(‎ ‎\\begin{array}{cc}‎ ‎\\Phi_{C,D}(A) amp; C \\\\‎ ‎C amp; \\Phi_{C,D}(B) \\\\‎ ‎\\end{array}‎ ‎\\right)‎ ‎\\end{equation*}‎ are positive‎, ‎for all positive operators $A$ and $B$ such that $D=A\\sharp B$‎.