The G-parity-violating, second-class current-(SCC) induced tensor term in the weak-nucleon axial-vector current was determined from β-decay correlation measurements of the mass A = 20 mirror pair. The alignment correlation terms in the β-decay angular distribution from the purely spin aligned mirror pair, 20 F and 20 Na, were measured in the present study. Combining the present results with existing results of β and delayed γ -ray angular correlation measurements for the A = 20 mirror pair, the SCC-induced tensor term was extracted to be d II /Ac = 0.18 ± 0.48. In the extraction, the weak-magnetism term, b/Ac = 8.58 ± 0.28, evaluated from the M1 analog γ -ray decay strength, was used in a framework of the conserved vector current hypothesis. This is the first unambiguous extraction of the (b − d II )/Ac term free from the contribution of the second-forbidden form factor, j 2 , in the axial-vector current, which was a limiting factor for accurate determination of nonexistence of the SSC in the β decay of the A = 20 system. K. MINAMISONO et al. PHYSICAL REVIEW C 84, 055501 (2011) cancellations [5,10], possibly due to uncertainties in the nuclear structure. Therefore, the search for violation should be undertaken in various mass systems. For this purpose, β-decay correlation measurements were performed in the A = 8 (β-α angular correlation) [11,12] and A = 20 (β-γ angular correlation) [13-17] mirror systems. The β-decay correlation terms were formulated to first order of recoil terms in Ref. [7] and expressions taken in the reference will be used hereafter in this article. Unambiguous extraction of SCC from those correlation measurements, however, has been rather difficult due to imperfect knowledge of the M1/E2 mixing ratio of M1 analog γ decays and poor statistical error of the γ -ray decay strengths, from which a second-forbidden form factor, f , in the vector current is evaluated under an assumption of CVC.An alternative procedure to extract the SCC-induced tensor term was recently introduced in the A = 8 system [18], where the alignment correlation terms in the β-decay angular distribution from nuclear-spin aligned 8 Li and 8 B were combined with the β-α angular correlation terms. The (b − d II )/Ac term and other coupling constants associated with higherorder matrices are independently determined by fitting both correlation terms simultaneously. Here b/Ac is the weak magnetism, d II /Ac is the SCC-induced tensor term with c being Gamow-Teller form factor and g T /g A = d II /Ac. This procedure, combining both correlation terms, is a more reliable way to extract the (b − d II )/Ac term than that with a single correlation measurement. It is noted that the SCC-induced tensor term always appears with the weak magnetism in those correlation type measurements, and therefore, precise extraction of the SCC-induced tensor term is possible only when the weak magnetism is well known.The alignment correlation terms of the A = 20 system, 20 F(I π = 2 + , T 1/2 = 11.07 s) and 20 Na(I π = 2 + , T 1/2 = 447.9 ms), were m...