Inheritance tax or Estate tax is on the estate of the person who dies, and nothing to do with the recipient. When the last of your parents die then any estate taxes due will paid out of their estate. Currently the federal estate tax is only on estates greater than $24 million for a married couple so unless their net worth is greater than that then no federal estate taxes will be due. Some States also have estate taxes so you will have to investigate that for the State in which they die.
https://www.investopedia.com/estate-tax-exemption-2021-definition-5114715One thing that will make things easier to manage is to ensure that they have beneficiaries and/or payment on death elections made on all their financial accounts. For example my wife and I each have IRAs and the beneficiaries elections are for the money to pass in total to the other, or if there is no spouse then then split evenly between our children. (Primary is spouse and Secondary beneficiaries are our children).
At any time they can gift money and property (e.g. shares) up to $16k per person per person without any reporting at all. More than that they would have to file an IRS gift tax report which will deduct the gift from their lifetime allowance. e.g. If 2 children were involved then each parent could gift $16k each to each of their 2 children meaning they could give $64k a year without any paperwork required.
When residents of the UK receive inheritances, or large gifts, then no UK taxes are due, simply report where the money is coming from when moving it to the UK, and that is true of any large movement of money. A few years ago when we transferred $250k to the UK from the sale of our US house we simply reported it to the bank as such, and also to the solicitor managing the purchase of our UK house.
