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In my opinion, it is not mandatory to mention the third party location in the offer letter. The third party location may keep changing during his tenure of working. This issue should not be of any concern since he has the offer letter of the company on whose payroll he is working and all the statutory obligations are met by them.
However, at the time of separation he can request his employer to mention the the clients name in the service certificate.
Hope your query is answered.
10th May 2017 From India, Mumbai
10th May 2017 From India, Bangalore