Cohomological subrepresentation injectivity conjecture

Let $K$ be a number field, let $p$ be a prime, let $M$ be a representation of $\operatorname{G}_K$ on a finite-dimensional vector space over $\mathbb{F}_p$, and let $S$ contain the primes above $p$ and those where $M$ is ramified. Let $K_\mathrm{cyc}$ be the cyclotomic extension, let $\Omega$ be the relevant coefficient ring, and let $Q$ be its field of fractions. Cohomological subrepresentation injectivity conjecture. For every $\operatorname{G}_K$-subrepresentation $N\subset M$, the map

$$Q\otimes_{\Omega}\operatorname{H}^2(\operatorname{G}_S(K),N_{K_\mathrm{cyc}})\longrightarrow Q\otimes_{\Omega}\operatorname{H}^2(\operatorname{G}_S(K),M_{K_\mathrm{cyc}})$$

is injective. This is proposed as a strengthening of the subrepresentation conjecture, intended to address descent issues under extensions of degree prime to $p$; its general validity is open.