This is a good article to read if you want to begin to understand why the law of conservation of energy cannot tell us whether the soul exists, much less whether it's immortal. (It describes what the law of conservation of energy actually refers to, as opposed to what New Agey types claim it means.)
To the best of our knowledge (and we literally have no compelling reason to think otherwise right now; and yes, that includes OOBEs) everything that makes us us is biochemically stored in our brains, and perhaps also in some other parts of our bodies.
Also, a lot of people who try to appeal to the law of conservation of energy are overlooking the simple reality that while matter and such cannot be destroyed, it can be transformed in such a way that whatever we consider to be its essence is lost forever.
Let's say for example that we have a diary containing years' worth of personal entries - the writer has encoded all sorts of information in it via their language and writing system of choice.
Now let's set that diary on fire, and let it burn thoroughly.
The atoms that made up that diary haven't disappeared; they still exist. But the fire tore them asunder and transformed them to the point where the text that was once written on the pages is now forever lost.
Plus, we also know that destroying the human brain destroys our memories and such; just look into what Alzheimer's does to people.
So, anyone who tries to appeal to the law of conservation of energy to try and claim the soul is immortal is either engaging in sophistry, or just doesn't know what they're talking about.