The SU(3)-flavor violating decay J/ψ→Ξ(1530)-Ξ++c.c. is studied using (1310.6±7.0)×106 J/ψ events collected with the BESIII detector at BEPCII, and the branching fraction is measured to be B(J/ψ→Ξ(1530)-Ξ++c.c.)=(3.17±0.02stat±0.08syst)×10-4. This result is consistent with previous measurements with an order of magnitude improved precision. The angular parameter for this decay is measured for the first time and is found to be α=-0.21±0.04stat±0.06syst. In addition, we report evidence for the radiative decay Ξ(1530)-→γΞ-with a significance of 3.9σ, including the systematic uncertainties. The 90% confidence level upper limit on the branching fraction is determined to be B(Ξ(1530)-→γΞ-)≤3.7%.