Acontece, @ Karlson está certo! Tem que ser menos de 6 meses. Exatamente 6 meses ou mais não é uma opção e não funciona.
Citando o @Karlson:
More then likely this is not going to work. When you enter the country let's say on August 11th, 6 months will end on February 10th and given the direction of travel and flights which usually happen overnight from US to UK you will arrive on February 11th, which since the timezone differences aren't likely to be taken into account will put your relative entering the US just one day over the 6 months limit with all the consequences stemming from it.