Depositing money in the name of her husband is a bad idea. In the US, an inheritance is separate property only if not combined with spouse's funds. It is in her best interest to keep it separate and in an account only in her name.

I suggest that until she gets her US immigration issues resolved, she would be best served by having you deposit her inheritance into her account in the UK.

If a banking institution chooses to do so, it can offer accounts to illegal aliens. The ITIN number is a Social Security like identifier that permits even illegal to file taxes.