I am not a party to a lease. The client died and I told the landlord I would try to find someone for the property. The landlord believes I am now responsible to may payment even to the lease ended for the client 3 months ago and died last month. I don't believe the landlord can hold me responsible for his rent but he thinks because I was trying to find a new teante that I am responsible for paying the rent.
Based on the information you have supplemented, the landlord is wrong. You don't specify your jurisdiction, but I highly doubt any legislation is odd enough to entitle the landlord to transfer liability to an entity which has no relation to the contract.
Since (1) the lease is only between the landlord and the deceased tenant, (2) you did not benefit as a tenant from that lease in its latest modality (i.e., month-to-month modality), and (3) there is no contract --be it in writing or as evidenced by your entity's conduct-- between you[r entity] and the landlord to support a presumption of tenancy insurance/hedging, the landlord has no viable claims against you or your entity. Your sole, voluntary offer to help find a new tenant is not binding and no legal duties arise from it.
He might have a viable claim only if your contract with the deceased tenant contains a provision resembling the aforementioned insurance. However, the existence of such provision seems unlikely for an agency that helps cash-strapped tenants.
The deceased tenant’s legal personal representative is responsible for the rent
The death of the tenant did not end the lease so the deceased tenant’s estate is responsible for it. The “legal personal representative” is the executor of the will or the court appointed administrator if the tenant died intestate.
Depending on jurisdiction, the death may give the landlord or the tenant or both the right to terminate the lease, for example, in New South Wales.
You were paying the rent. Clearly there was some sort of arrangement with someone for you to do this - that arrangement might be a contract if it satisfies the elements or it might give rise to promissory estoppel. Similarly, so could your undertaking to “find someone for the property”, particularly if you asked the landlord to do something for you - like hold the property.
If so, then the landlord is right.