If the deceased family member who held shares in his/her own name (single) had left a will, how do the legal heir/s get the shares transmitted in their names?

The legal heirs will have to get the will probated by the Court of competent jurisdiction and then send a copy of the probated will, along with relevant schedule/annexure setting out the details of the shares, the relevant share certificates in original and transmission form for transmission. A and B held shares of Brawn Pharmaceuticals Limited. Both of them died. How do I get the shares transmitted in my name?
You should obtain a Succession Certificate/Letter of Administration of the last deceased joint holder in your favour and follow the procedure for transmission of shares.