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Are you asking if you are liable?
The landlord is under a duty to mitigate his loss by seeking a replacement.
You can't make him liable per se though. What you do is argue that you should not be liable for the entire months remaining on the basis that he did not mitigate his loss. Usually a landlord is expected to find a replacement within one month or maybe two at the highest. They will not get away with just refusing to market the property and claiming from you.
Can I clarify anything for you?