Hi! I am American, living in the UK and have US citizenship and leave to remain in the UK and am really experienced with this.
It is very complicated.
First off, any US citizen has to file something called an FBAR with the IRS which shows any money held in a foreign account or offshore investments. Hopefully she has been doing this because the penalties are severe if she hasn’t.
You can hold 10k in a calendar year outside the US without getting taxed by the IRS, but you have to disclose it.
I am not sure how the HMRC treats money held in US accounts but it is worth talking to a tax advisor who specialises in US - UK taxes. I have spoken with Tax Advisory Partnership based in the UK - they specialise in US - UK taxes.
Now onto investing.
Personally, I only invest in US based investment because any income I make from them will go into my US accounts and remain in the US and therefore will only be taxed in the US.
However, I have recently learned that as soon as I start to file in both the US AND UK (currently I do not have to file in the UK and I won’t for another few years) - then I am subject to UK taxes on worldwide income. Which presents a problem for my US investments.
There is a company called Thunn Financial which specialises in US - UK investing. I have not spoken to them yet but I will.
My understanding from researching is that there are only a handful of funds that are NOT subject to dual taxation. A lot of these are vanguard index funds. It really limits your options.
If you google “US and UK investments that aren’t double taxed” you will get a lot of good information about it.
The most important thing is that she continue to file with the IRS and talk to a tax advisor! Because the worst thing would be if she invested in a fabulous fund and then got hit with 40-50 percent taxation when she sells because of dual US / UK tax.
Good luck, please feel free to PM me if you have more questions.