What is used as basis for stock acquired by estate after death of decedent

The decedents brokerage account was set up to receive dividends as shares of stock.  I changed this to receiving cash but prior to this some stock was received.  Normally, the basis is set to the value on date of death for inherited stock and you can put "inherited" for basis.

1) When I distributed this brokerage account only full shares were transferred and 0.955 shares remained.  This was cashed out resulting in a gain that was distributed to the beneficiaries.  The 1099B  used the date a dividend was purchased as stock for the basis for the 0.955 shares - which is 3 months after death.  I assume I use the actual basis on the purchase date instead of date of death as well?

2) - When transmitting stock to heirs I have told them the basis on the date of death is the basis to use.  For any shares acquired after date of death do I need to first determine who received those exact shares and then tell them the actual basis and date of purchase?