If we consider 'kamma' as intention and habits, how are these transferred from a brain to next life when the brain breaks-up and cease to function?

The texts say nothing because "rebirth" in original Buddhism does not mean "reincarnation". "Rebirth" means the "re-arising" of "self-belief" based on acts of kamma and their results.

The original Buddhist scriptures say mind cannot exist without a material body:

Were someone to say, 'I will describe a coming, a going, a passing away, an arising, a growth, an increase, or a proliferation of consciousness apart from form (materiality), from feeling, from perception, from fabrications,' that would be impossible.

SN 22.53

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It's good, monks, that you understand the Dhamma taught by me in this way, for in many ways I have said of dependently co-arisen consciousness, 'Apart from a requisite condition, there is no coming-into-play of consciousness.'

Consciousness, monks, is classified simply by the requisite condition in dependence on which it arises. Consciousness that arises in dependence on the eye & forms is classified simply as eye-consciousness. Consciousness that arises in dependence on the ear & sounds is classified simply as ear-consciousness. Consciousness that arises in dependence on the nose & aromas is classified simply as nose-consciousness. Consciousness that arises in dependence on the tongue & flavors is classified simply as tongue-consciousness. Consciousness that arises in dependence on the body & tactile sensations is classified simply as body-consciousness. Consciousness that arises in dependence on the intellect & ideas is classified simply as intellect-consciousness.

MN 38

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Very well then, Kotthita my friend, I will give you an analogy; for there are cases where it is through the use of an analogy that intelligent people can understand the meaning of what is being said. It is as if two sheaves of reeds were to stand leaning against one another. In the same way, from mind-&-body as a requisite condition comes consciousness, from consciousness as a requisite condition comes mind-&-body.

SN 12.67

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The four great elements, bhikkhu, are the cause and condition for the manifestation of the body aggregate.... Mind-and-body is the cause and condition for the manifestation of the consciousness aggregate.

SN 22.82

Aren't intention and habits a function emerging form the conjuncted activity of brain cells?

I haven't ran across any Sutta that says Nama (name or immateriality like feeling, perception, mental formation) are properties that emerge out of Rupa (form or materiality). In Buddhism, the Five Aggregates can be said as operating together, but it'd be invalid to say that the mental part arises or "emerge" out of the material part. A crude analogy is like electricity and the light bulb. While the operation of various light bulb components allow for the manifestation of electricity, it'd be invalid to say that electricity "emerges" out of the light bulb. Another example is the radio wave and the physical radio. Its components allows the manifestation of sound and music, but it'd be invalid to say that the radio "creates" the sound and music. It's due to this certain degree of independence between Name and Rupa that makes it's possible for the Kammic stream to carry on from life to life.

To phrase traditional Mahayana understanding in modern words, Mind and tendencies ("samskara" & "karma") are not "inside" the brain, instead they are media-independent informational/causational phenomena.

They exist "in" and underlie the very fabric of material processes at all organizational levels (dhatu).

Human beings, as well as inanimate objects, and also group entities, and other biological and social phenomena, serve as media or carriers or agents for the informational processes spanning many such carriers (as e.g. brains, books, computers) across space and time.

Mind is not "inside", matter/energy and information/mind are two sides of the same coin. I claim that this is the traditional perspective of Mahayana, whether many active practitioners can articulate it like this or not.

Intention and habits do not "originate" from the brain cells of course. They exist as latent tendencies in the realm of information and manifest via action mediated by a living organism with a brain (usually) or sometimes by other means at other organizational levels.

If person A tells person B a message, person B then gets this message, understands it and remembers what he understood of it. But we cannot say that this message was physically transferred from A to B. All that was physically transferred were movements of air molecules as sound waves. The message was conceptually transferred and not physically transferred. The message is a conceptual entity and not a physical entity. We also cannot say that the message that B had and the message that A had are exactly identical, because B might have understood the message slightly differently. Also, we are able to trace the history of the transmission of the message, for e.g. from A to B to C etc.

Also, similar is the transfer of a flame from one candle to another. Physically, the heat from one burning candle ignited another candle's wick, causing it to start burning. But we cannot say that the flame itself transferred from one candle to another. The flame here as something that moves from one candle to another is again a conceptual entity and not a physical entity. We created the concept of the flame. In physics, it's simply plasma emitting from a burning wick. As the candle burns, the plasma ions get replaced. There is no single physical entity as the flame. The flame from one candle is also not identical to the flame of another candle that it ignited. We can also trace the history of transmission of the flame from one candle to another. So, the transfer of the flame from one candle to another is also a conceptual transfer and not a physical transfer.

So too is "rebirth" in Buddhism. It's not a physical rebirth or physical transfer, but a conceptual rebirth or conceptual transfer. Similarly what a "being" or "person" or "self" is, are also concepts. If person C is reborn and now becomes person D, person D and person C are not exactly the same, yet not completely different, just like the message that transferred from A to B. And it is possible through attainments of meditation, to trace the history of transmission from C to D.

Instead of using the term "rebirth", I prefer to say that suffering or dukkha continues beyond physical death, and that suffering or dukkha is only ended by Nibbana, and not ended by physical death.

To understand this you need a complete paradigm shift in the way you are thinking. Stop looking at the world in terms of entities. Drop everything that you think is real involving entities and start looking at the world in terms of experiences arising and dying. In this world you have six types of experiences: seeing, hearing, smelling, tasting, feeling(tactile) and thinking. You have firsthand knowledge that arising of these experiences is real because they can be sensed. Once you make this paradigm shift, you will understand that the brain is not an experience. The brain cannot be sensed. It is nothing more than a concept fabricated in a thought. No direct knowledge can be gained by building theories based on fabrications. So the question of what happens to the mind when the brain is dead does not arise as it doesn't exist in the first place.

Karma is not a thing that is transmitted anywhere. Karma is simply the volitional action involved in each experience. That volitional action dies with the experience. But it can give a result immediately or in the future. You need to do Satipatthana meditation to see this happening. Ex: if a pleasurable experience arises and you get attached to it, suffering follows when it dies. This is the immediate Vipaka(result) of the Karma you just committed. In the future also if you cannot get this experience, suffering will arise. This attachment also creates a habit of doing things to get similar experiences. This gives rise to new experiences involving fresh Karma.

It is impossible to understand the complete dynamics of Karma unless you become a Buddha yourself, but when you start looking at the world through meditation, you will see that this continuous arising of experiences goes on and on until you cut off what is fueling them to arise. I.e. craving. Even though we do not have complete comprehension, this understanding of Karma is enough to work towards ending of suffering.

In this framework, the medical definition of death becomes just another concept involving entities. You will see that as long as there is craving, the arising of new experiences will never stop. Once the thought pattern makes this paradigm shift, questions like how the mind is transferred to a new body after death etc. do not arise as there is no constant thing called the 'mind' and there is no constant thing called the 'body'. The reality is made up continuous arising of experiences. These experiences have a physical aspect and a mental aspect. They arise due to causes. Read the Paticcasamuppada to get an intellectual understanding and do Satipatthana meditation for direct knowledge.