I humbly believe that my answer here might be partially or completely wrong.
There are three types of Karma - Sanchita karma, Prarabdha karma and Kriyamana karma.
Sanchita karma is karma accumulated over numerous lives of the aatman.
Prarabdha karma is a portion of the collected Sanchita karmas which will be experienced by a living entity during its lifetime.
Kriyamaana karma is the karma which an individual can create during their lifetime.
Citing from Wikipedia (although I do not believe Wikipedia is a great source in such scenarios)
"In Vedantic literature, there is an analogy. The bowman has already sent an arrow and it has left his hands. He cannot recall it. He is about to shoot another arrow. The bundle of arrows in the quiver on his back is the sanchita; the arrow he has shot is prarabdha; and the arrow which he is about to shoot from his bow is agami. Of these, he has perfect control over the sanchita and the agami/Kriyamana, but he must surely work out his prarabdha. The past which has begun to take effect he has to experience."
To answer your question,
- Karma is the cause of one’s suffering
I believe that you might have misunderstood Karma. In the scenario of Pn wronging Pn-1 :
- Say Pn was wronged by Pn-1 and Pn is suffering because Pn-1 had done something wrong against Pn in his past life.
So Pn who had done something adharmic in a previous life against Pn-1 accumulated certain paapa(bad) karmas which became Sanchita, and later became Prarabdha karma and experienced suffering in his lifetime from the reborn Pn-1.
Now, it is certainly possible in their previous lives where Pn-1 wronged Pn(hence Pn suffering in current life), Pn-1 might have done certain ill deeds as Kriyamana karma - that is, from his mind and judgement, and not because of Prarabdha karma. This is the origin of that karma, as it was Kriyamaana.
Karma is not simply a luggage carry over from one life to another, it is possible to add more such luggage to the aatman or remove luggage (either through burning of karmas by suffering, or innumerous other methods described over thousands of years)
That is why it is believed that in the Kali yuga, humans are less understanding of Dharma and Karma, and actively create more karmic luggage through their Kriyas (Kriyamana karma) which simply gets added on as Sanchita karma, and later experienced as Prarabdha karma.