It's a very simple process actually.

Step 1 - Open both Power Armor Is A Privilege andthe mod you want to patch in FO4Edit.

Step 2 - Find the Object Modification section of the Power Armor mod you want to patch.

Step 3 - Find all of the Linings (they should be labelled something like A, B, C, D, E, F or something like that (I've also seen authors use MK. I, MK. II, MK III etc...etc...). I do not believe you have to do this for the standard linings, as it does not appear that PAIAP does this either so in all of my patches I have refrained from doing so as well.

Step 4 - Copy all of these as overwrites into a new esp/esl file. Skip this step if you are going to edit the power armor mod directly.

Step 5 - Right click on either the Power Armor mod or the newly created patch esp/esl in the left pane of FO4Edit and in the pop-up window click "Add Masters." Add Power Armor Is A Privilage as a master to the file.

Step 6 - Click on a lining in the left pane. In the right pane of FO4Edit, find the Properties (sorted) section.

Step 7 - Add the following property to that section.

Value type: Form ID, Int

Function type: ADD

Value 1- Form ID: EnchPA_Damage_Resistance "Power Armor Damage Resistance" [ENCH:0A006CE2] (for "non-raider style" power armor) or EnchPA_Damage_Resistance_Raider "Power Armor Damage Resistance" [ENCH:0A006CE3] (for "raider style" power armor)

Value 2 - Int: 608

Step: 0

And just do this for each lining of each power armor lining.

An easy way to copy/paste this is the do it for a couple lining, then shift click to select ALL of them in the left pane. Then right click and at the top of the pop-up menu click "Compare Selected". It should bring up all the linings and their differences allowing you to copy, drag and drop the newly added property from the already edited linings to the ones still needing to be edited.

Step 8 - Cower in fear any time you come across an enemy wearing power armor in the wasteland.