The following is true, look up:
Dawe GS, Tan XW, Xiao ZC. Cell migration from baby to mother. Cell Adh
Migr. 2007;1:19–27. [PMC free article] [PubMed]
The scientific name of this process is called microchimerism, defined by another study as:
the presence of cells originating from another individual therefore genetically distinct from the host cells, is a phenomenon seen during pregnancy whereby fetal stem cells pass bidirectionally from fetus to mother and these microchimeric stem cells persist for many years, influencing the immune status of females in relation to transplant therapy
The conclusion of the study was the following:
Fetal cells exhibit a remarkable ability to migrate across the placenta into the mother and to integrate with diverse maternal tissues and organs, apparently homing in particularly to sites of damage and disease. Much remains to be learned about the basic biology of fetomaternal microchimerism. The cell type or types involved have yet to be conclusively characterized. If various cell types are involved, it will be important to understand the time course of the migration of the various cell types and their persistence in the mother. Studies of the process of cellular adhesion and migration that allow the cells to cross the placental barriers, infiltrate tissues and organs, cross the BBB and migrate to sites of damage will be especially informative. Although long-term persistence of fetal cells may be less frequent in the mouse, the mouse appears to offer a useful model for investigating aspects of fetomaternal traffic during pregnancy.