Does it have built-in housing, or just holes?
If there's a path for the cable, not just holes, you can probably lube it up and shove it through. Make sure there's a clean cut on the cable (no strands sticking out; maybe even solder or super glue the last half-inch to hold it together), then poke it in one end and use pliers to jam it along a little at a time until it pops out the other.
If you just have holes, and you have to hit one from the other . . . well, that's why my Trek is a singlespeed now. I pulled the internal housing for the rear derailleur out of the chainstay and tried for two years to get it back in. Finally I said the hell with it and converted to SS. But here are some ideas people posted when I asked about it:
--Just keep poking until you hit it (that's how I wasted two years).
--Put a stiff wire through, then attach the cable to the wire and pull it through (couldn't hit the hole, which was only a frac of a millimeter bigger than the cable.
--Insert wires with loops in the ends into the tube from BOTH ends, hook them and pull them out (at least in a chainstay, the diameter was too small to maneuver. I couldn't hook up).
--Put dental floss in one end and a vacuum cleaner hose on the other and suck the floss through the hole. Tie a string to that and pull the string through. Tie the string to the cable and pull the cable through. (Couldn't suck out the floss).
Your holes may be larger, and the diameter of a handlebar is bigger than a chainstay, so one of those might work for you.
