Prompt-fission-neutron spectra from $^{239}\mathrm{Pu}$ ($\mathit{n},\phantom{\rule{0.16em}{0ex}}\mathit{f}$) were measured with respect to $^{252}\mathrm{Cf}$ spontaneous fission for incident neutron energies from 0.7 to $700\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$ at the Weapons Neutron Research facility (WNR) of the Los Alamos Neutron Science Center. A newly designed high-efficiency fission chamber was coupled to the highly segmented Chi-Nu neutron liquid scintillator array to detect neutrons emitted in fission events. The double time-of-flight technique was used to deduce the incident neutron energies from the spallation target and the outgoing-neutron energies from the fission chamber. Prompt-fission-neutron spectra (PFNS) were measured with respect to $^{252}\mathrm{Cf}$ spontaneous fission down to $200\phantom{\rule{0.16em}{0ex}}\mathrm{keV}$ and up to about $12\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$ for all the incident neutron energies with typical total uncertainties well below $2%$ up to about 7-MeV outgoing-neutron energy. The general trend of PFNS is well reproduced by JEFF3.3 and ENDF evaluations, although a better agreement is found with JEFF3.3. Discrepancies were observed for the low-energy part of the spectra, especially around the opening of the second-, third- and fourth-chance fission. Neutron average kinetic energies as a function of incident neutron energy are obtained experimentally with reported total uncertainties below $0.5%$. The measured values agree with the most recent data. The trend is fairly well reproduced by the JEFF3.3 evaluation, although it fails to reproduce the experimental values within their uncertainties.