We report on the implementation of a spectral phase transfer scheme from near IR to deep UV, in which the frequency conversion step is based on the broadband phase-matched four-wave mixing in a gas-filled hollow core waveguide. Micro joule level femtosecond pulses at 260 nm were generated by nonlinear mixing of a Ti:sapphire laser and its second-harmonic. The transfer of a π-step phase in a controllable manner was proposed and confirmed by a modulation observed in the generated deep UV femtosecond pulse spectrum due to an interference process. Numerical simulations confirmed our results.