Assembly Press is by far the safest method of press fitting components without misalignment and breakage. Press fit the brass ferrule into the end of the short inner tube. Place this aside for a moment. Put the open end of the cylinder first. Make sure it is pressed all the way in, so that the brass ferrule is even with the top of the blank.
Press fit the mechanism top into the long inner brass tube.
The mechanism stop must be flush with the end of the tube. Insert the open end of the inner tube into the finished blank and press until the inner tube is flush with the bottom of the finished barrel. To advance the lead, hold the bottom barrel and turn the top barrel.