TD Handbrake (& MGA)

[Ed McCarroll <EMCCARROLL@magnum.mco.edu>]

        I'm glad the question was asked re. greasing handbrake cables.
        My MGA has what looks like an armored wound outer sheathing
        for the cable.   The outer sheathing has a grease nipple (Zerk
        fitting).   Problem is that when I put a grease gun to lube
        it the grease travels only a short distance along the inside
        of the sheathing before comming out at the winding joints.
        I am using lithium grease.   Should I be using something else
        or is there some technique I should be using for better results?