Can you transfer stock to a family member?

Yes, you can transfer stock to a family member. If you are the shareholder, you can transfer the stock to your nominee or the legal heir. Proofs for legality like Succession certificate, Legal heir certificate, etc., must be produced in order to transfer your stock to your nominee or the legal heir.
In case of nominee, the documents required for transfer of stocks are: Affidavit worth Rs.200/-, Indemnity bond, Aadhaar card and PAN card of the nominee, residential proof.
In case of legal heir, the documents required for transfer of stocks are: Affidavit worth Rs.200/-, Indemnity bond, No objection certificate, Legal heir certificate, Aadhaar card and PAN card of all the family members along with residential proof.