I always used Phil Oil. and of course my method was different. I would leave the FW on the wheel, and lay it on the bench. turn the cogs so it 'freewheels' and drop the oil in between the moving outer body and inner body.
I remember seeing the grease fitting tools but never used one.
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“One morning you wake up, the girl is gone, the bikes are gone, all that's left behind is a pair of old tires and a tube of tubular glue, all squeezed out"
Sugar "Kane" Kowalczyk