What exactly do they want to convert / preserve ?
Libs / Sch / Pcb / Net ?
I have seen Altium to KiCad, but not the reverse, so you may be best to look into expanding on the Altium to Kicad paths with your own code, but full Sch and Pcb convert will be non-trivial.
eg The Icezum project converted fromAltium using this
Netlist extract should be relatively simple - ie to confirm a Design finished in KiCad, started in Altium.
eg I have done PcbNew -> Mentor PADS ASCII NET, to confirm a PADS -> PcbNew Pathway.
Also note that translators are not usually "100.0% push-button", they issue warnings on entities that only almost/mostly translate and errors on entities that cannot translate directly.
That means you would need Altium to check the conversions.
Another approach is to try to find a CAD pgm that can import KiCad, that Altium can also import.
KiCad is changing fairly rapidly, so that may be quite an ask...