I moved last week and found that the movers lost a nipple that couples
two internally threaded rods. These rods are part of a wardrobe rack
that's several years old. I can't find the manufacturer's name on the
rack and I've spent a lot of time visiting hardware stores and looking
online for the nipple. You can see a picture at
http://www.teksor.fi/kuvat/12035.jpg that looks exactly like what I
need: about 3/4" long, 3/4" diameter, 16 threads-per-inch.

Connect two "internally" threaded rods?

Depending on the threads, I would either cut a section of threaded rod to
the length I need, or I would check the plumbing section for a 3/4"
'close' nipple. Either should be available at any home center or hardware
store.

Anthony