  We have analyzed primary $\gamma$-ray spectra of the odd-odd $^{238}$Np
nucleus extracted from $^{237}$Np($d,p\gamma$)$^{238}$Np coincidence data
measured at the Oslo Cyclotron Laboratory. The primary $\gamma$ spectra cover
an excitation-energy region of $0 \leq E_i \leq 5.4$ MeV, and allowed us to
perform a detailed study of the $\gamma$-ray strength as function of excitation
energy. Hence, we could test the validity of the generalized Brink-Axel
hypothesis, which, in its strictest form, claims no excitation-energy
dependence on the $\gamma$ strength. In this work, using the available
high-quality $^{238}$Np data, we show that the $\gamma$-ray strength function
is to a very large extent independent on the initial and final states. Thus,
for the first time, the generalized Brink-Axel hypothesis has been
experimentally verified for $\gamma$ transitions between states in the
quasi-continuum region, not only for specific collective resonances, but also
for the full strength below the neutron separation energy. Based on our
findings, the necessary criteria for the generalized Brink-Axel hypothesis to
be fulfilled are outlined.
