In Buddhism, it's a consciousness that keeps continuing and reappearing conjoined with material which grow in another form.

There's nothing eternal in Buddhism. It's all anicca (impermanence), dukkha (dis-ease), anatta (non-self). So no way there's eternal soul/spirit.

It's about nama-rupa (mental component and material component) which work according five niyama Dhamma (The laws of the universe which is 1.Utu Niyama, 2.Bija Niyama, 3.Kamma Niyama, 4.Dhamma Niyama, 5.Citta Niyama).