In the paper "Poincaré duality and commutative differential graded algebras" Lambrechts and Stanley constructed PD model for cdga with simply connected cohomology. My question is: if $A$ and $B$ are two quasi-isomoprhic CDGA, and  $\hat{A}$ and $\hat{B}$ be their PD models respectively, are $\hat{A}$  and $\hat{B}$ quasi-isomorphic as PD algebras?