We demonstrate the transfer of a shaped spectral phase in a pulse with a sub-20-fs pulse Fourier limit of a Ti:sapphire laser to that in a deep UV pulse at 256 nm in a sum- frequency-mixing process. The generated UV pulse maintains a sufficiently broad spectrum to form a sub-20-fs pulse due to broadband sum-frequency mixing with the group-delay-dispersion-matched scheme. The spectral phases of the deep UV pulse are measured with spectral phase interferometry for direct electric field reconstruction and compared with the phase applied to the Ti:sapphire laser pulse.