You could see if they are interested in framing as is in a deep frame, as a kind of testiment to it's history.
Often insurance covers conservation treatment, they might speak to their adjuster. Depending on size etc. it might not be all that much to send it to a conservator, unless anything over $25.00 would be too much.
To try and flatten it themselves (and I'd suggest that the owner rather than you try it as you're not getting paid to do it and so are taking on needless risk/possible angst for no compensation?)it would likely be the old humidify and press treatment.
As other have suggested, humidity chamber - many variations on how to build one, the idea is to have the item exposed to high humidity for a day or so, so that the paperboard (it is paperboard isn't it?) can absorb the moisture evenly and slowly and relax a bit. (Watch out for condensation dripping on front!) Then sandwich between blotters, or white matboard, cover with rigid material like 1/4" glass or plexi, or plywood..., and weight. Change blotting material every day or so until it is quite dry (or warp will come back).
That is the simplest version - there are lots of varients like humidifying with Goretex, using spunbond polyester release sheets to avoid possible blocking, blowing warm air through corrugated interleaves, I know some framers use heat and their press to speed up the drying process. Sometimes the treatment needs to be repeated 2 or 3 times.
A lot of it is just having the materials on hand and often it is cheaper to have someone who has the materials do it than gather them all together one's self.
Good Luck.
Rebecca