I am with Martin - although I put the grease in the outboard end. I squirt a slug of silicone grease from a syringe in the prop end of the tube then push the shaft through. You have to wipe the grease off the inboard end of the shaft before connecting the motor, but I have had no leaking on the half dozen boats I have used this method on. I don't try and fill the whole tube, but I am not sure how far the grease actually extends when the shaft is in place - about a third of the way along I would guess.
Greg