Is it permissible for the son to remain with the divorced woman, who was granted custody by the court, after she remarries, given that she lives in a European country that allows her to keep the son with her?

If a custodial mother marries, her right to custody is forfeited, and custody transfers to the next rightful person. This is the Sharia ruling, and any law contradicting it is not to be considered. However, the child may remain with her if the person who has the right to custody agrees and the new husband approves, provided that the child's best interest is ensured.