Neither of them seems to have a specific background in neuroscience.
Suzanne Mays seems to have an education background in applied medical secretarial science, which in no way qualifies her to study human consciousness. They don't mention having a specific background in neuroscience and seem to mainly work as a music practitioner. Robert Mays doesn't mention having any background in neuroscience, psychology, or even just medical science. He mainly has a background in chemistry and software development.
What you cited also doesn't seem to be a study from a reputable scholarly journal either. It's from a website whose reliability is questionable, based on some of the content on there. It doesn't help that they seem to have work published in the
Journal for Scientific Exploration. This journal has been criticized for publishing pseudoscience and generally seems to have a bad reputation overall. These do not seem to be two individuals whose research and claims should be trusted.
@Darkover is right. So far scientific consensus is that consciousness arises from brain activity. There is no evidence for things like reincarnation, as far as the modern-day scientific community is concerned.