I suppose if a conscious mind experiences consciousness in another universe at the exact same moment that it is experiencing the same consciousness here, then it would not be the same consciousness. But then again, how can it be the same time in another universe as it is in our Universe. I don't think time works like that.
Since consciousness is a brain process, rather than a thing, I don't see how a conscious mind that existed in our Universe could not also exist in another Universe. It wouldn't have to obey the laws of physics. Even if our Universe were the only current Universe, a conscious mind could potentially reappear after death many trillions of light years away (assuming an infinite Universe) immediately after death. The speed of light would be no obstacle.
Similar to what you wrote above: if someone claims that it is impossible for a conscious mind to return again after its current body dies, even if time is infinite, then they are claiming that the conscious mind is impossible. Anything that is possible is guaranteed to happen an infinite number of times through infinite time, otherwise it's impossible. I know I'm not impossible.
I'll quote what I wrote a few years ago concerning this version of reincarnation and the extremely low odds that I could exist at this very moment if I only ever got one life:
Reincarnation and the Multiverse
"When I was young I thought it interesting that I was alive at that moment. With only one life the odds were greatly against my existence at that or any particular time, considering how old our Universe is. During most of the life of our Universe I hadn'tt existed (as far as I knew). I hadn'tt yet thought about reincarnation.
Lets say that our Universe is the only universe and time will soon end. With only our Universe and one life, someones chances of existing at a particular time (with a 75 year life span & our 13.8 billion year old Universe) are 1 in 13,800,000,000/75 = 1 in 184,000,000. Lotteries have much better odds than that.
But the odds get much worse. Our Universe will likely be around extremely far into the future, many times its current age if not forever. Imagine an infinite time-line to the future representing all of time that will probably ever exist. Let's say that there is no reincarnation and we only get one life. What are the chances that I would be alive at a particular moment if I had only one life on the infinite time-line? It is zero, since (one life time)/(total time Universe will exist) = finite#/infinity = infinitely small number = zero, which would be the odds of me living right now with only one life and our Universe exiting forever into the future.
So it would be impossible for me to be conscious right now if I only got one life and time is infinite. Since my consciousness existing right now is very important for my consciousness, my existence right now is the equivalent of me winning the lottery with zero odds of winning. So it seems with infinite time I must be reincarnated an infinite number of times for it to be possible for me to exist right now."