Fiber optics help

[1996Z15]

I have had an issue with my left front turn signal not working lately and it turned out to be a bad socket. I purchased a new turn signal assembly from Paragon that came assembled with new light bulb, gasket, lens and the amber glass bead that connects to the fiber optic cable.
I have removed my old signal assembly and was able to push the amber glass bead (still attached to the fiber cable) out the back of the old socket.
Now I need to know how do I safely remove the fiber cable from the original amber glass bead and transfer it to the new unit without damaging anything?
I am hoping to get this taken care of soon so the car is ready for Kerbeck's Toy's for Tot's run on 11/4.