Soul (Atma, Atman)

Soul (Atma in Hindi, Atman in Sanskrit) is just another name for Brahm, often used in the context of being present inside living beings.

I don't think there is a one-to-one mapping between Atma and body. It is not appropriate to say there is "one" soul inside every body. This is like saying there is "one" gold inside every gold bangle (gold is like Brahm/Atma, gold bangle is like the body). A more appropriate way to say this would be,"body is made of Atma". Hence, there cannot be a one-to-one transfer of the soul from an old body to a single new body after death.

There is also a colloquial usage of the term "soul" which refers to the integrity or the conscience of a person (as in "selling one's soul"). This seems to stem from the above mentioned belief that there is "one" soul inside every person, that guides him on the right path. I think this is a simplistic way of looking at soul and perhaps the root of much confusion. Decisions and emotions are controlled by brain and mind; soul is simply the underlying building block that makes the whole living being, including his body/brain/mind.