We employ a variational Monte Carlo approach to efficiently obtain the dynamical structure factor for the spin-1/2J1-J2 Heisenberg model on the square lattice. Upon increasing the frustrating ratio J2/J1, the ground state undergoes a continuous transition from a N\ue9el antiferromagnet to a Z2 gapless spin liquid. We identify the characteristic spectral features in both phases and highlight the existence of a broad continuum of excitations in the proximity of the spin-liquid phase. The magnon branch, which dominates the spectrum of the unfrustrated Heisenberg model, gradually loses its spectral weight, thus releasing nearly deconfined spinons, whose signatures are visible even in the magnetically ordered state. Our results provide an important example on how magnons fractionalize into deconfined spinons across a quantum critical point
