My rear tire Presta valve began giving me some problems this morning. I noticed that the top screw (typically unscrew/screw this to inflate/deflate) was screwed too tightly to the valve pin thread and subsequently to the core. With a pair of pliers I was able to get the screw off but with it came the thread from inside the valve. I know how to screw the core back into the tube thread, but can't figure how to get the valve thread to attach/stay inside the core so that I can put it all back together and inflate the tire?
Have attached a picture showing the tire stem, the vale core, and pin thread/screw so you can understand how things have come apart.
Any thoughts on how to get the thread back together with the valve core?