Kate said to me that she had finished my book. and that it had been very interesting
the teacher said that the Earth went round the moon. (это не правда, Земля вращается вокруг Солнца, поэтому делаем шаг назад)
The British Prime Minister said that Russia was/is a great country. Если в предложении говорится о непреложной истине, то не надо делать шаг назад. Действительно ли в предложении непреложная истина решать Вам.
My friend asked me if I should come to your place or to stay at home.