You might want to seek professional guidance in your locality.
https://taxexperts.naea.org/listing/service/estates-gifts-trusts
Regardless, in the typical scenario, the shares would be stepped up to their fair market value as of the date of death. Further, the dividends can, most likely, be reported as income in respect of a decedent (IRD) at this point.
https://www.irs.gov/publications/p559#en_US_2021_publink100099582
Doing so would simply involve reporting the dividends as such on your individual income tax return (Form 1040).
