Pelikan Toledo piston repair

[mresimulator]

Hello!

 

I have this Pelikan Toledo, presumably from the 80s.

as you can see from the pictures attached, the piston mechanism is partially disassembled. When I assemble it, the back knob doesn’t contract fully.

If am I right, the only way to get it right is remove the thread black part attached to the barrel, then to assemble the piston mechanism outside the barrel (considering get the fully contactin of the back knob) and then insert the fully assembled mechanism into the barrel. Is that correct? If yes… what the right way to do it? Are that thread part friction fitted into the barrel or thread into it? Left or right thread? 
Should I apply dry heat and or DW40?

if it is friction fit… should I apply pressure from the section extreme using a wood bar o apply pull tracción from the back thread part? Piston contracted or extended?

 

thanks a lot!!!