We recently reported an association of offspring educational attainment with polygenic risk scores (PRS) computed on parent’s non-transmitted alleles for educational attainment using the second GWAS meta-analysis article on educational attainment published by the Social Science Genetic Association Consortium. Here we test the replication of these findings using a more powerful PRS from the third GWAS meta-analysis article by the Consortium. Each of the key findings of our previous paper is replicated using this improved PRS (N = 2335 adolescent twins and their genotyped parents). The association of children’s attainment with their own PRS increased substantially with the standardized effect size, moving from β = 0.134, 95% CI = 0.079, 0.188 for EA2, to β = 0.223, 95% CI = 0.169, 0.278, p < .001, for EA3. Parent’s PRS again predicted the socioeconomic status (SES) they provided to their offspring and increased from β = 0.201, 95% CI = 0.147, 0.256 to β = 0.286, 95% CI = 0.239, 0.333. Importantly, the PRS for alleles not transmitted to their offspring — therefore acting via the parenting environment — was increased in effect size from β = 0.058, 95% CI = 0.003, 0.114 to β = 0.067, 95% CI = 0.012, 0.122, p = .016. As previously found, this non-transmitted genetic effect was fully accounted for by parental SES. The findings reinforce the conclusion that genetic effects of parenting are substantial, explain approximately one-third the magnitude of an individual’s own genetic inheritance and are mediated by parental socioeconomic competence.