Very Very Old Small Carved Arm, Believed Egyptian Middle Kingdom

This small carved arm, clearly once jointed to a figure, I purchased from an artist and collector a couple of years ago and have lived with since. He purchased it from a gallery while working on a project in Egypt, along with an ancient carved and painted falcon (which I am keeping forever) and said he was certain it was ancient--and looking at that wood, and also at the form of the arm and hand, it certainly appears he was right. I've included a couple of photos in documentation for reference--carved figures, and a carved arm, both described as Egyptian Middle Kingdom, 12th Dynasty, 1991-1783 B.C. I'm in awe of things so old that have endured--a small fragment here, but just right that it should be a hand, seemingly reaching out across time, whatever it once held onto long gone from its grasp. 4 3/4" long. Stable and not particularly fragile.