Explanation:
The B allele will become more common only if the individuals reach reproductive ages
Since the individuals with allele B have much greater reproductive success therefore once they reach the reproductive age, success to reproduce new individuals will be higher
The offsprings will carry on the allele(B allele) and pass on to the next generation
Even if the parental individuals die because of shorter life span the offsprings produced in each generation will pass on the allele to their subsequent generation