All hell breaks loose

1. A putative evidence for reincarnation are cases of individuals who have corroborated memories of a past life. I haven't examined any case-studies to verify that claim, but suppose we grant the phenomenon for the sake of argument. Christians often default to demonic possession as the explanation. Suppose we consider that first. Here's one objection:

He accentuates the fact (if it is a fact) that cases of reincarnation involve personal continuity whereas cases possession involve personal discontinuity. 

https://triablogue.blogspot.com/2009/03/possession-reincarnation.html

A problem with Almeder's objection is the basis on which he makes those classifications. It seems to be circular. Do the phenomena themselves provide evidence for that distinction, or is he applying his classifications a priori to the phenomena, where he simply assumes the continuity/discontinuity distinction? How does he know possession is inconsistent with less continuity?

There are, however, other objections to the demonic explanation. Offhand, there's no reason to assume a correlation between a particular demon and a particular decedent whose memories a living person shares. Why would a demon have such intimate knowledge of the decedent? The demon might have such knowledge if both the decedent and the living person who shares those memories are possessed by the same demon, but we'd need evidence that's the case.

2. A more direct explanation for why some people have memories of dead people (assuming, ex hypothesi, that's the case) is that the souls of damned (i.e. human souls) sometimes take possession of the living. 

Some Christians object because they don't think the damned are allowed to contact the living. But there's no theological reason to deny that possibility. The church age is a mixed up time. The saints and the damned aren't separated in this life. The realm of light makes incursions into the realm of darkness while the realm of darkness makes incursions into the realm of  light–like a lighthouse at night. 

The ability of damned souls to contact the living doesn't mean hell has a back door, if we're using "hell" in the technical sense of the final state of the damned. An absolute separation between the two groups only takes place at the day of judgment, not the moment of death.