We derive the equations of motion for the bulk-to-boundary propagators of the anti-de Sitter (AdS) boson and fermion fields with arbitrary total angular momentum J in a soft-wall AdS/QCD model and solve it analytically. It provides the opportunity to study transition form factors induced by these bulk-to-boundary propagators, both for on-shell and off-shell hadrons. This is a continuation of our study of hadron form factors induced by the bulk-to-boundary propagator with total angular momentum J=1 (e.g., electromagnetic form factors of mesons, nucleons, and nucleon resonances).