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There has always been much debate and relgious consternation of when a Soul leaves a body at death and the circumstances surrounding departure. It seems to always some down to belief and there are multitudes of them.

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My information is based on past life regressions I do as a hypnotist and books on this subject, I do not offer any psychic services - please look for a medium, shaman or a psychic online or in your vicinity to check on your loved ones who passed or to clear you or your house from attachments or ghosts. - Irina Nola

Typically it happens immediately after death, especially if the person was dying from illness and already said their goodbyes. They still might linger for several days appearing to relatives, especially children who are very open to seeing spirits. Some spirits stay longer if they had unfinished business, or want to stay around the family or the tribe. Tribal spirits can stay much longer as in shamanic belief they have duties as Ancestors helping the tribe - they receive healing in natural places and can stay in physical reality up to 100 years (about 3 generations) and can either reincarnate into the same tribe or cross into the Spirit World and plan a life in a different culture. If the tribe was killed - they all receive healing and reincarnate in the same land but in other races - I have a lot of my American past life regression clients who were Native American in a past life and reincarnated as white or black people in the same territory, as they have a strong bond to the land.

Some spirits never cross over and either attach to a living person or to a place or building, becoming ghosts. (Earthbound spirits) They can get rescued by their Guides, but if their vibration is very low or if they refuse to go into the Light for any reason - a living person with psychic abilities in necessary to help them (a shaman or a medium) - as they can reach them on the low astral plane and persuade them to cross over, in this case, their Guides or Guides of the medium can ‘pull them” into the Light, providing the energy for the transition.

https://www.quora.com/How-long-does-it-take-for-the-soul-to-cross-over

All this natrurally graduates to: 

How long does it take to reincarnate?

According to Spiritual Teacher June Marshall -

Every soul has its unique path of expansion and growth. Human concepts, such as time, do not apply to the Soul. The Soul is eternal and always exists in the eternal Now. So for anyone to determine how long it takes for a Soul to reincarnate is an exercise in absurdity. Time does not apply in this situation.

Each reincarnation depends on so many things. And if a Soul has finally reached the end of their karmic path it may not choose to reincarnate at all. It may choose to remain in pure cosmic consciousness or pure positive energy. Or it may be completely karmically clean and decide to reincarnate anyway to help others on their journeys. These are known as bodhisattvas.

Dr. Helen Wambach, Ph.D., was one of the earliest scientific researchers into past lives and reincarnation. She was the author of Reliving Past Lives and Life Before Life.

In Life Before Life Dr. Wambach described the results of hypnotizing 750 people and taking them to the time between their past and current lives. One of her findings was that the disembodied consciousness, or soul does, not enter the body until near birth. "The soul usually enters the body near birth, and has a choice of which fetus to enter. If one fetus is aborted, it is possible to choose another. In some cases, the soul who will occupy the fetus, is in contact with the soul of the mother, and can influence her decision regarding abortion."

Dr. Wambach found that 89% of those hypnotized said they did not become part of the fetus until after six months of gestation. A large group said they did not join the fetus, or experience inside it, until just before or during the birth process. They existed fully conscious as an entity apart from the fetus and even after six months many reported being 'in' and 'out' of the fetal body.

"Many subjects reported that the onrush of physical sensations on emerging from the birth canal was disturbing and unpleasant. The soul exists in a quite different environment in the between-life state. The physical senses bring so much vivid input that the soul feels almost 'drowned' in light, cold air, sounds.”

She reported that, “The new-born baby feels cut off, diminished, alone compared to the between-life state. To be alive in a body is to be alone and unconnected. Perhaps we are alive to learn to break through the screen of the senses, to experience while in a body the transcendent self we truly are."

https://www.quora.com/When-someone-dies-how-long-does-it-take-to-reincarnate-into-a-new-body