Here is <A HREF="https://math.dartmouth.edu/~jvoight/notes/Waldspurger.pdf">Sur les coefficients de Fourier des formes modulaires de poids demi-entier</A>    
and here is <a href="https://www.imj-prg.fr/IMG/pdf/waldspurger1983.pdf">Correspondances de Shimura</A> (not the 1980 paper, but a summary of that paper from 1983)