Those aren’t fonts.
Thats what I thought. However the client is hell bent on saying they are. It's funny how many "graphic designers" dont't know how to properly format, or export their work. I think this going to get messy.
another is a .bmap and another doesn't have any extension,
Those may have been fonts, back in the 20th century. There certainly were fonts that ended in .bmap, circa Win 3.1/Mac OS 7, I think. That was a long time ago - so long that I can't even recall which platform used the extension. I suspect that it'd have to be Windows, right? Anyhow, there is pretty much no chance whatsoever that you will be able to get it to work, if it actually is a font file. On the other hand, perhaps both of you are correct and they are not fonts at all - the .lst file is, for sure, not a font.
A four letter file extension, on Windows, in the 20th century? Nah.
These are bitmap representations created with the Font Switcher/Chooser, created from some ancient font file (probably Old Type Apple Truetype fonts) so you could use them in a prehistoric version of the Mac OS.
It's Arcane Knowledge as well that these files on themselves are of no use at all without the outline originals. An entire generation of graphic designers has grown up making exactly that mistake.
Could you give us the filenames?
Postscript fonts consist of two files -- a "suitcase" of bitmaps and the "printer" font. The bitmaps file could have any extension; people would change them to whatever they wanted. I've also seen ".suit" or ".fam". The printer font does not have an extension and the name would be a shortened version of the full name of the typeface (for instance "HelveConBlaObl" for Helvetica Condensed Black Oblique).