cross-level interaction in lme4

Dear All,

In the model below, I have a cross-level interaction (SES of students x
MEAN SES of schools). However, MEAN SES of schools is made from SES of
students.

So, my question is: Is such an interaction: appropriate, meaningful, and
legitimate?

hsb <- read.csv('
https://raw.githubusercontent.com/rnorouzian/e/master/hsb.csv')

library(lme4)
m1 <- lmer(math ~ ses * meanses + (1|sch.id), data = hsb)

Thank you,
Simon