Moreover, kamma is not stored in something and taken to the next life. You are acknowledging that there is an absence of an inherent element (soul), but you are thinking
as though it must be there between two consecutive lives. The dhamma (ultimate reality) of it is, there isn't anything. At the end of one life, or a series of mental fluctuations, the aggregates (which synthesize experience) breakup. However, the kammic energy of those fluctuations has been transfigured just so, and the residual potency of all that unexpressed volition makes the consciousness just so, and that kamma instantaneously expresses itself with the arising of another being, spawning another life under the according conditions
. A successor to the kammic lineage, that's all. His, or hers or its, first instant of consciousness is conditioned by the rebirth-linking consciousness, or the final instant of the predecessor.
Beings do not arise for no reason, they arise as a result of kammic energy (volitional potency), and being thus conditioned they continue to produce this kamma.
I hope I was not confusing?