Reason for registration?

You need to amendment the gst certificate registration after giving intimation in gst portel. after that you will get fresh certificate under new name.
The legal representative of deceased person Will be liable for payment of tax due, interest penalty if any
refer sec 93 if CGST.

Before surrendering the GSTn of Proprietor ,, you have to file ITC 02 for transfer of any balance lying in credit ledger & the same will be reflected in Son"s Portal under ITC 02 , Accept it for successful transfer.

No need to pay Tax On stock : While filing of cancellation , Reason for cancellation select the option death of Proprietor , (Change in constitution) .
It will not ask you to deposit tax on Stock.

For detail explanation on the same Kindly Refer circular 96/15/2019 GST