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Wiktionary
front organization

n. An organization which secretly acts as the public face of a covert group.

Wikipedia
Front organization

A front organization is any entity set up by and controlled by another organization, such as intelligence agencies, organized crime groups, banned organizations, religious or political groups, advocacy groups, or corporations. Front organizations can act for the parent group without the actions being attributed to the parent group thereby allowing them to hide from public view.

Front organizations that appear to be independent voluntary associations or charitable organizations are called front groups. In the business world, front organizations such as front companies or shell corporations are used to shield the parent company from legal liability. In international relations, a puppet state is a state which acts as a front (or surrogate) for another state.