The Central Depository Services (India) Limited through a scroller on their website, has informed that once KYC is done through a SEBI registered intermediary (this includes a broker, Depository Participants, Mutual Fund etc.), the same process need not be undergone in case another intermediary is approached. KYC is a onetime process that needs to be done while dealing in securities market.
Source: Central Depository Services (India) Limited
