Finiteness conjecture for LERF groups with Kazhdan property (T)

Let $G$ be a countable group with Kazhdan property (T). Finiteness conjecture. The group $G$ is LERF if and only if it is finite.

By the preceding proposition, for groups with property (T), LERF is equivalent to A-separability, so the conjecture asserts that this phenomenon cannot occur for an infinite group with property (T).