Willi, they already have CS6, and CC will not install on XP, so it would be a wast of time and effort to try to move to a newer version without also doing a hardware/OS upgrade.
I suspect we need Joel here to confirm, but my suspicion is these are very old non-Unicode-compliant fonts, though why they work when not converting is a bit of a mystery to me.
In any case, I installed the fonts here temporarily on Windows 7 and opened the file in PM7. It shows three fonts in use. When I open the file in ID, it comes in missing fonts, but shows only a single font, SH, which is not either of the fonts listed in Pagemaker. I can use Find Font to replace with the supplied fonts, but I still have missing font problems in scattered areas, and the Glyphs panel does not register even the glyphs that show. I'm tempted to chalk this up to typical PM-to-ID conversion problems.
On the other hand, exporting the story to RTF in PM, then importing that into ID seems to work. That's certainly not as convenient as a direct conversion, but probably the way to go.