Formal equivalence conjecture for extensions of codifferentials

Let $d=d_2+d_k$ be a codifferential, and let $d_e=d_2+d_k+d_l+\cdots$ and $d_e'=d_2+d_k+d_l'+\cdots$ be extensions. Two codifferentials are formally equivalent when a formal automorphism expresses an equivalence between them. Formal equivalence conjecture. If $d_e'$ is formally equivalent to $d_e$, then $d'_l-d_l$ is the leading term of a $D$-coboundary for the coboundary operator $D=[\bullet,d]$. This is a classification tool for codifferentials: it identifies the first difference between formally equivalent extensions as a coboundary. The supplied text gives no resolution, so the conjecture remains open.