It seems that the ProShow Producer professional slideshow making software allows export of the shows (.phs) to MPEG-4 format (.mp4), which means psh to mp4 conversion is certainly possible. However, we couldn't find any other software that would be capable of this conversion, so using the original ProShow remains your only choice.
Convert ProShow Producer slideshow to MPEG-4 video file format.
We have found one software suitable in our database for this conversion.
Microsoft Windows software - convert psh to mp4 on Windows
A software used to create professional slideshows
Convert from psh file format
The table with program actions contains information about what each program is capable of doing with their files. This may be a good pointer for further searches for certain file conversions and help you find the converter you are looking for if our search result is insufficient for you. However, it is far from perfect and may sometimes show results which are not really usable because of the nature of the software handles the files. So a conversion that appears as possible, just because of matched actions, may in fact not be possible.