In his book The g Factor (pg 169), Arthur Jensen wrote:

The broad heritability of IQ is about 0.40 to 0.50 when measured in children, about 0.60 to 0.70 in adolescents and young adults, and approaches 0.80 in later maturity.

Rushton & Jensen write:

…the default hypothesis, is that genetic and cultural factors carry the exact
same weight in causing the mean Black–White difference in IQ as they do in
causing individual differences in IQ, about 80% genetic–20% environmental by
adulthood.

Elsewhere they write:

Jensen (1998) demonstrated that Black-White IQ differences typically increase with age (because genetic influences become stronger over the life span). He used Shuey’s (1966) compendium to document that the average
Black-White difference was 0.70 standard deviations in early childhood, 1.00 standard deviations in middle childhood, and 1.20 standard deviations in early adulthood…

…Until the results of several such studies allow reassessment of the situation, the best estimate of Black-White convergence over the past 100 years is between 0 and 3.44 IQ points—a maximum effect size of 0.23—well within the predictions of our estimated heritability of .80 for the Black-White g difference in the United
States.

Rushton & Jensen seem to be saying that because IQ is only 20% environmental (among U.S. whites), the 15 to 18 IQ point black-white U.S. IQ gap could at most, only be expected to close by 20% (3 to 3.6 points), thus reducing the gap to only 12 to 14.4 points .

One problem with this theory is that 80% means the proportion of IQ variance explained by genes so you need to take the square root to get the regression line predicting genetic IQ from phenotypic IQ which means differences would actually be 90% genetic, allowing only a 10% decline in the black-white IQ gap, assuming you believe a) heritability is 80%, and b) the default hypothesis is true.