Summary: In recent papers, we have studied the quantum-mechanical decay of a Schwarzschild-like black hole, formed by gravitational collapse, into almost-flat spacetime and weak radiation at a very late time. In this recent work, we have been concerned with evaluating quantum amplitudes (not just probabilities) for transitions from initial to final states. In a general asymptotically flat context, one may specify a quantum amplitude by posing boundary data on (say) an initial space-like hypersurface \(\Sigma_I\) and a final space-like hypersurface \(\Sigma_F\). To complete the specification, one must also give the Lorentzian proper-time interval between the two boundary surfaces, as measured near spatial infinity. We have assumed that the Lagrangian contains Einstein gravity coupled to a massless scalar field \(\phi\), plus possible additional fields; there is taken to be a ‘background’ spherically symmetric solution \((\gamma_{\mu\nu},\Phi)\) of the classical Einstein/scalar field equations. For bosonic fields, the gravitational and scalar boundary data can be taken to be \(g_{ij}\) and \(\phi\) on the two hypersurfaces, where \(g_{ij}\) \((i,j=1,2,3)\) gives the intrinsic 3-metric on the boundary, and the 4-metric is \(g_{\mu\nu}\) \((\mu,\nu=0,1,2,3)\), the boundary being taken locally in the form \(\{x^0=\text{const}\}\). The classical boundary value problem, corresponding to the calculation of this quantum amplitude, is badly posed, being a boundary value problem for a wave-like (hyperbolic) set of equations. Following Feynman’s \(+i\epsilon\) prescription, one makes the problem well-posed by rotating the asymptotic time interval \(T\) into the complex: \(T\mapsto |T|\exp(-i\theta)\), with \(0 <\theta\leq\pi/2\). After calculating the amplitude for \(\theta>0\), one then takes the ‘Lorentzian limit’ \(\theta\to0_+\). Such quantum amplitudes have been calculated for weak \(s=0\) (scalar), \(s=1\) (photon) and \(s=2\) (graviton) anisotropic final data, propagating on the approximately Vaidya-like background geometry, in the region containing radially outgoing black-hole radiation. In this paper, we treat quantum amplitudes for the case of fermionic massless spin-\(\frac12\) (neutrino) final boundary data. Making use of boundary conditions originally developed for local supersymmetry, we find that this fermionic case can be treated in a way which parallels the bosonic case. In particular, we calculate the classical action as a functional of the fermionic data on the late-time surface \(\Sigma_F\); the quantum amplitude follows straightforwardly from this.