In the essay "Buddhist Reflections on Death", V.F. Gunaratna wrote:
The terminal thought goes through the same stages of progress as any other thought, with this differences that whereas the apperceptive stage of complete cognition known as javana or impulsion, which in the case of any other thought occupies seven thought-moments. At this apperceptive stage the dying person fully comprehends the death-sign. Then follows the stage of registering consciousness (tadalambana) when the death-sign is identified. This consciousness arises for two thought-moments and passes away. After this comes the stage of death consciousness (cuti-citta). Then occurs death. This is what happens in this existence.
Now let us consider what happens in the next existence. Already the preliminaries for the arrival of a new being are in preparation. There is the male parent and there is the female parent. As explained previously a third factor, a psychic factor, is necessary to complete the preliminaries for the arising of a live embryo, and that is the relinking consciousness (patisandi-viññana) which arises in the next existence in the appropriate setting — the mother's womb. On the conjunction of these three factors, life starts in the mother's womb. There is no lapse of time, no stoppage of the unending stream of consciousness.
As I understand, the last consciousness of a lifetime (cuti-citta) and re-linking consciousness (patisandhi-viññana) are terms coming from the Abhidhamma. They explain the continuity of the stream of consciousness from one lifetime to the next. This together with bhavanga and javana (see here) explains the continuity of the stream of consciousness between thought-moments both in this lifetime and the next lifetime, and between the two.
On the other hand, MN 38 seems to imply that there is no continuity of consciousness and that consciousness arises conditionally based on dependent origination.
The Blessed One then asked him: “Sāti, is it true that the following pernicious view has arisen in you: ‘As I understand the Dhamma taught by the Blessed One, it is this same consciousness that runs and wanders through the round of rebirths, not another’?”
“Exactly so, venerable sir. As I understand the Dhamma taught by the Blessed One, it is this same consciousness that runs and wanders through the round of rebirths, not another.”
“What is that consciousness, Sāti?”
“Venerable sir, it is that which speaks and feels and experiences here and there the result of good and bad actions.”
“Misguided man, to whom have you ever known me to teach the Dhamma in that way? Misguided man, have I not stated in many ways consciousness to be dependently arisen, since without a condition there is no origination of consciousness? But you, misguided man, have misrepresented us by your wrong grasp and injured yourself and stored up much demerit; for this will lead to your harm and suffering for a long time.”
So, how does the Abhidhamma reconcile the concept of re-linking consciousness (patisandhi-viññana) with MN 38 above?
Also, even in the current lifetime, is there any real continuity of consciousness or does it merely appear so?