reincarnation, page-29

"this is wrong understanding because "becoming" is a mental state rather than a new life"

If by "becoming" you mean Bhava then it has a far greater meaning than simply a mental state. Bhava occurs with every moment of conciousness and is either Kammabhava - producing Kamma - or Uppattibhava - neutral Kamma.

Bhava also relates to the realms of existence in which rebirth can take place - Kamma Bhava, Rupa Bhava and Arupa Bhava.

Death unfortunately does not bring an end to this process of "... becoming; birth; old age, sickness and death" because the process itself is like "cause" and "effect". As long as there are causes, effects will happen. Death does not alter this. It is just part of the process. What we generally refer to as death is one special moment in this process when this physical body can no longer be sustained. In reality every moment of consciousness "dies" and then a new one occurs. With "death" it happens to be that the next moment after death in in a different form or body.

So, Bhava has a broad meaning which refers to the kind of existence in which consciousness can arise, but also is part of the process that occurs with every conscious moment. Until one is free (vimutti) from this process (Paticcasamuppada) Bhava will continue to ocurr, even after death.