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? According to the Pali Canon, how are intentions and habits passed on from one existence to another without any material support?
What do the texts tell us about rebirth and the transference of these material phenomena into inmaterial phenomena, and the back to material ones?

More specifically,  how is kamma transmitted from one life to the next. If we consider 'kamma' as intention and habits, how are these transfered from a brain which, as you observed, is destroyed and dissolved after the breakup of the body? Aren't intention and habits a function emerging form the conjuncted activity of brain cells?

Thanks in beforehand.
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.