I love the works of Prof Conway and I am so sad because of this happening. This is not an answer, but a nice things about him that shows his attractive personality. This was told by Prof Peter Cameron in his blog:
This happened at a conference somewhere in North America. I was chairing the session at which he was to speak. When I got up to introduce him, his title had not yet been announced, and the stage had a blackboard on an easel. I said something like "The next speaker is John Conway, and no doubt he is going to tell us what he will talk about." John came onto the stage, went over to the easel, picked up the blackboard, and turned it over. On the other side were revealed five titles of talks. He said, "I am going to give one of these talks. I will count down to zero; you are to shout as loudly as you can the number of the talk you want to hear, and the chairman will judge which number is most popular."
So he did, and so I got to hear the talk I wanted to hear.
RIP John, the world is a poorer place without you.
A very nice memorial about Prof Conway by Princeton university: