He is not legally liable to find a replacement tenant for you. But he cannot lie to you either - find a tenant but getting money from both of you. If he does this I think he is committing something illegle.
When you made the decision to move out early, you should have expected to 'lose' the rest of the rent money already. If you can find someone to take over your lease that's great, but if not you cannot expect your landlord to be liable in anyway either.
Good luck.