Who might have received Constantinople after a successful Dardanelles campaign?

If the Dardanelles campaign had succeeded, would Britain have given Constantinople to Russia or Greece?

Russia is considered unlikely to receive it, with Greece more plausible; the immediate strategic purpose was to help keep Russia in the war.

Greece is suggested as the more likely recipient of Constantinople in this counterfactual, while transfer to Russia is doubted. The immediate strategic priority was to keep Russia in the war. The proposed eventual settlement and the wartime purpose of forcing the straits are separate questions.