Adem's integral collapse conjecture for cyclic group extensions

Let $C_n$ be a cyclic group of order $n$ and let $L$ be a finite-rank integral lattice. For a split group extension

$$0\to L\to \Gamma\to C_n\to 1,$$

let $\{E_*,d_*\}$ denote its Lyndon–Hochschild–Serre spectral sequence, with coefficient modules in $\mathcal{M}_F(L,C_n)$. Adem's integral collapse conjecture. The spectral sequence $\{E_*,d_*\}$ collapses at $E_2$ for all such coefficient modules. This question was posed by Adem and remains open for arbitrary finite cyclic groups; the paper discusses it in the context of results on differentials and collapse for split group extensions.