Unless barred by the co-op bylaws, it is legal. Illegal immigrants can own property in or invest in the United States--their immigration status does not affect that. Therefore, they can be co-op owners and, if owners, can be board president.That said, making himself and the treasurer beneficiaries fo the co-op's money likely illegal on several grounds: a violation of fiduciary duty, a violation of co-op law, possibly a form of theft.