Transfer of maternal antibodies to the fetus is a well-known and documented finding. It is not surprising that antibodies to SARS-Cov-2 from a vaccinated mother would cross the placenta to the child.
As Gary Lee Gilmore pointed out, antibodies are known to cross from the mother to the fetus. After birth, babies continue to acquire antibodies from their mother's milk.
In the case of SARS-Cov-2, there have been several studies that have examined the presence of neutralizing antibodies in this context. For example, this cohort study from Harvard found that the mRNA vaccines from Moderna and BioNTech both resulted in antibody transfer (primarily IgG) into fetal blood (testing umbilical cord blood at delivery) and breastmilk. Preprint COVID-19 vaccine response in pregnant and lactating women: A...
Transfer of SARS-CoV-2 antibodies from the mother to her fetus, as in some other infectious diseases, is well-known and documented (Maternal Immunity). Such antibodies to SARS-CoV-2 could cross the placenta from the recovered or vaccinated mother to the fetus.