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High-contrast imaging (HCI) observations of exoplanets can be limited by the island effect (IE). On the current generation of telescopes, the IE becomes a severe problem when the ground wind speed is below a few meters per second. This is referred to as the low-wind effect (LWE). The LWE severely distorts the point spread function (PSF), significantly lowering the Strehl ratio and degrading the contrast. In this article, we aim to show that the focal-plane wavefront sensing (FPWFS) algorithm, Fast and Furious (F&F), can be used to measure and correct the IE/LWE. We deployed the algorithm on the SCExAO HCI instrument at the Subaru Telescope using the internal near-infrared camera in H-band. We tested F&F with the internal source, and it was deployed on-sky to test its performance with the full end-to-end system and atmospheric turbulence. The performance of the algorithm was evaluated by two metrics based on the PSF quality: 1) the Strehl ratio approximation ($SRA$), and 2) variance of the normalized first Airy ring ($VAR$). Random LWE phase screens with a peak-to-valley wavefront error between 0.4 $μ$m and 2 $μ$m were all corrected to a $SRA$ $>$90\% and an $VAR\lessapprox0.05$. Furthermore, the on-sky results show that F&F is able to improve the PSF quality during very challenging atmospheric conditions (1.3-1.4'' seeing at 500 nm). Closed-loop tests show that F&F is able to improve the $VAR$ from 0.27 to 0.03 and therefore significantly improve the symmetry of the PSF. Simultaneous observations of the PSF in the {optical} ($λ= $ 750 nm, $Δλ=$ 50 nm) show that during these tests we were correcting aberrations common to the optical and NIR paths within SCExAO. Going forward, the algorithm is suitable for incorporation into observing modes, which will enable PSFs of higher quality and stability during science observations.