Imagine a person that is very calm, generous, doesn't like to harm others etc. If this person gets a rebirth in the human realm will he/she develop the same characteristcs?
The point is that Kamma and the last mental state can go on, but according to Anatta I'm not sure about the rest.
kamma doesn't actually go on. kamma means action, and it is finished after it is performed. Nothing actually goes on from one moment to the next; the effects of one moment are felt in the next, and have potential repercussions far into the future.
It is these repercussions that do indeed create a sense of continuity from life to life; a person who ended their life with a certain nature will be reborn with a similar nature, simply due to the causal nature of reality.
"Bhikkhus, whatever a bhikkhu frequently thinks and ponders upon, that will become the inclination of his mind."
MN 19 (Bodhi, trans)
I've heard this issue described as one of the major philosophical problems for Buddhism. How does rebirth make sense in the absence of a fixed self? The problem is akin to the problem of evil for Christians - how does a good God allow bad things to happen. And as fitting this kind of problem there's been a lot of historic opinion and arguably no definitive answer.
The thoughts and analogies that I have found useful have been
One position is that there is rebirth but no-one is reborn. I fit this satisfying mystical to be honest.
The analogy of the candle. A new candle is lit from an old one and the flame passes from candle to candle. We can't say it's the same flame but then we can't say that the flames in the candles are unrelated. The contention is that this is an instructive way to think about rebirth.
Another analogy of a pile of coins versus a string of beads. Reincarnation (with a soul) can be viewed as a string of beads. There is something (the thread/a soul) that runs through all beads. A pile of coins is like rebirth (no soul). There is nothing running in the pile of coins that gives them their location in the pile. However it is the positions of all the previous coins that gives the uppermost coin it's elevated position.
If none of these work then there is always the Buddha's advice about not worrying about such metaphysical mechanics. Knowing this stuff won't help you get liberated.
I am aware that Tibetan Buddhists will have a far more definite idea about how these things happen. The perspective of this answer is probably more Theravadan but the book that I've sourced this from is more eclectic and even secular (Exploring Karma and Rebirth by Nagapriya ).
Looking at it from another angle, what would it mean to be reborn without your nature? In what sense would the reborn being still be you? Rebirth without persistence of nature is indistinguishable from no rebirth at all.
Everything is impermanent, even one's nature. If you look at the span of your life, your year, your month, or even a single day in your life you will see that your nature is in a constant state of change.
Agree with @Christopher Lee on this but with a small addition.
Some strong habits can persist over may lives and even after enlightenment, but in the long run they can also fade away.
Nature doesn't move. Your thinking is moving. You cannot think about your nature, you cannot speak about it, because your thinking is a "product" made from the nature by your tendencies which again raise from your habits.
We need to perceive our nature to understand it. Not to think about it. It's like to think about meals instead to eat.
Your nature appears when you stop the mess in your head.
Right now!
Enlightenment
Helping others
Congratulations! :-)
