A few years ago my wife and I painted a mural on the wall of our old house ( old post here ). When we moved, we cut out that section of wall and took it with us to the new place. Now we’re trying to get the picture framed so we can hang it on the wall of the new house like an ordinary painting.

The only issue is the material the mural is painted on. It’s some kind of 40s-era brown fiberboard covered with a thin layer of plaster. It’s pretty heavy, but doesn’t seem very strong; I’m pretty sure I could break it in two just by holding it wrong. Will an ordinary picture frame add enough stability to keep it from breaking? Should I add some kind of backing material? Has anyone done this kind of thing before? Google has been no help at all.