@Antoine Soverie,
@yaugie
Back with answers!
1. If you reassign a settler from one department to another and they have trained up the secondary stat, that training
does not apply to the new department.
Example: A Facilities Department staff has the Strength Stat as the Primary Stat required for providing department energy. The secondary stat for Facilities is Perception and that person was trained to use their Perception Stat through HQ Staff training to improve their energy rating.
Moving that person to Administration, that person will now use their Charisma as the Primary Stat to provide energy for that department. The secondary stat for Administration is Empathy, so the HQ training they received previously doesn't apply in their new department.
2. Confirmed: If you assign that settler back to their old department, their previous training will apply.
Added a note about Reassignments to the WIki.