I’ve wondered what the situation is for an expat living in Europe and inheriting US assets. But I don’t know where to look.
There will almost certainly be a double taxation agreement between that country and the USA
https://www.gov.uk/guidance/inheritance-tax-double-taxation-relief
If both the UK and another country charge Inheritance Tax, you could avoid or reclaim the tax through a double taxation convention.
As to the op’s question on gifting, the giftee will need to know the rules in the country he lives in. In the UK you can gift as much as you want in any given year with no tax consequence. However a 7 year clock starts ticking and if you die within 3 years and your Estate is above the limit then a tax of 40% is imposed on that gift. In years 4 through 6 the tax rate declines so that no tax is ever due on any size gift if the giftee is still alive after 7 years.