Variance of squarefull numbers in short intervals II

In this paper, we continue the study on variance of the number of squarefull numbers in short intervals $(x,x+2\sqrt{x}H+H^2]$ with $X\le x\le 2X$. We obtain the expected asymptotic for this variance over the range $X^{\epsilon }\le H\le X^{\mathrm{0.180688...}}$ unconditionally and over the optimal range $X^{\epsilon }\le H\le X^{0.25-\epsilon }$ conditionally on the Riemann Hypothesis or the Lindelöf Hypothesis.