It seems that, in those days, the "papers" published by the Notices were just some kind of abstracts. They are not collected on the internet. If you really want to read it, you should look for it in an university library. Nevertheless, according to Fiedler in Numerical Range of Matrices and Levinger’s Theorem (Linear Algebra and its Applications 220, 1995), there is no proof of Levinger's theorem in the notice you are looking for; but you have one in the very same paper of Fiedler, which you can locate here:

http://www.sciencedirect.com/science/article/pii/002437959400073M

I have read that paper by Fiedler. Thank you