By telegram! LOL. I need to try that one.
If blood transfusions had been available back then - she wouldn't have hesitated to give her son blood.
I've always suspected that was exactly what he was doing. Not by telegram, but when he went in the room with the doors closed. I think he did a meditation routine to calm the child (which could naturally slow the speed of, but not stop, the bleeding by slowing the heartbeat). Then I think he gave transfusions. Transfusions had been done a few hundred years earlier, and right around the turn of the century, experiments were getting more popular. A family with this level of resources could perhaps get any treatment they wanted. I think Rasputin gave transfusions and then told the family he was doing it by his own magical powers, as a way to ingratiate himself to this powerful family. Just my hypothesis!