If the value is more than no option except filling Succession Suit under provision of Indian Succession Act
You have to pay court fee as per your state court fee act
If you start today process will take min. 5 - 6 months
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1) When you get succession certificate attach and sent it to registrar and transfer share agent of the company.
2) They will insert name of all successor behind share certificate as mentioned in Succession certificate , tell them to insert name in same order in all certificates
3) Open Share Demat account
4) Dematerialize all certificate by filing concern form
5) Once all shares are dematerialised it will be reflected in Demat account
6) Open another Demat Account , and with signature of all concern transfer to specific demat account as per all your mutual understanding.
7) Matter is closed .
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First get help of local advocate to get succession certificate
Second get help of sub-broker of stock exchange he will do that demat work happily .
Third and most imp. thing this physical shares conversion to demat started long back , so search in house if any other physical shares remaining do it in one go only such old obsolete things no one knows latter how to do and they became lot complicated . In my opinion you are atleast 20 years behind schedule for demat