The Department of Natural Resources shall make a careful investigation of every body of water, both river and lake, in the State, and ascertain to what extent, if at all, the same have been encroached upon by private interests or individuals, and wherever it believes that the same have been encroached upon, the Department shall commence appropriate action either to recover full compensation for such wrongful encroachment, or to recover the use of the same, or of any lands improperly or unlawfully made in connection with any public river or lake for the use of the People of the State. The right and authority hereby given and created shall not be held to be exclusive, or to take from the Attorney General or any other law officer of the State the right to commence suit or action.