Is it permissible for a Muslim woman to communicate with her son, who was raised in a disbelieving family, and inform him that she is his mother, and would that be considered a violation of Sharia?

It is permissible for the woman to maintain ties with her son, and it is obligatory upon her to inform him of the reality of his lineage and invite him to Islam. If he responds, she should inform him of the invalidity and prohibition of adoption, and that it does not establish mahramiyyah (unmarriageable kinship) or inheritance.