Hi @stefano.tronci,
The zero solution for the real part may be correct, since you have a lossless material and the Neumann condition is purely imaginary. Does your Elmer solution also assume a lossless material? I note that the tutorial mentions that it is possible to include a damping factor D.
As for the weak form, it seems that the accepted solution in the thread you linked gives the same weak form that I derived. The post by @BillS is stated to be for a lossless medium; perhaps these two weak forms become equivalent when there is no damping?