Re-cabling a cheap grip-shift-a-like
 

The only brand ID on the shifter is the word "Power", no Sachs, Sram, Microshift labels.
I managed to access cable anchor by shifting the brake lever inboard and splitting the parts of the shifter apart with a thin blade. I also had to remove a snap-in plastic cable guide cover to route the cable through it's 90 degree bend. Inside, the cable had been sharply bent just as it exited the anchor, making the shifter inoperable and requiring some need-nosed plier activity to remove the cable.
Altogether the worst type of shifter to re-cable and what should have been a simple, routine task took about 40mins of struggle. Whoever designed this shifter should be put up against a wall and shot, and I don't mean in a nice way.

Have you tried to recable a Falcon shifter? The guy that desiged that should be drawn and quatered.

how about a picture? We might be able to give better advice. Good luck.