I have a threaded boom arm 5/8 in diameter,
I want to mount my strobes to it.
Is there thread inside the female end of this fitting?
No threads whatsoever. You'll need to replace your threaded boom arm with a 5/8" length of steel or aluminum rod stock, which you can buy inexpensively at your local Homo Depot building materials store. Once you've replaced the threaded boom arm with the 5/8" rod stock, you just slip the female hole on the grip head over the shaft of your rod stock and tighten the knob on the grip head and you're ready to go. Hmmm...the rod shaft goes into the female opening which clamps down on the shaft...if this wasn't a mechanically based answer, it would have to be thoroughly redacted for its apparent x-rating content.