Inverse wavelet transform on wavelet coefficients
Because, as far as I know, there is no discrete wavelet scheme related to the morlet wavelet, admitting neither orthogonal nor biorthogonal implementation. See for instance the discussion in Complex Morlet function and DWT.

Using waveinfo('morl'), you indeed get that: DWT: no

 Information on Morlet wavelet.
    Morlet Wavelet 
    Definition: 
    morl(x) = exp(-x^2/2) * cos(5x) 
    Family                  Morlet
    Short name              morl

    Orthogonal              no
    Biorthogonal            no
    Compact support         no
    DWT                     no
    CWT                     possible

    Support width           infinite
    Effective support       [-4 4]
    Symmetry                yes


So you might obtain something only (and I am not sure it is valid for your data) using some form of inverse continuous wavelet transform, for instance in Matlab  icwt.