What is the ruling on inheritance in the case where a maternal uncle adopts his sister's daughter, and is she allowed to refuse the inheritance?

Adoption, which is forbidden in Islamic law, does not entail inheritance. Therefore, your mother has no right to inherit from her maternal uncle who adopted her, unless the heirs voluntarily give her something. If the division of the inheritance requires referring the matter to governmental bodies that would grant her a share of the inheritance according to official documents, and you are unable to invalidate the adoption, then she should receive this inheritance and hand it over to the heirs so they can divide it according to the Shariah-prescribed shares.