Prime Material Dragon

Any effect that would inflict damage to a player instead increases their Life Points by the same amount. When a card's effect to destroy a monster(s) on the field is activated, you can send 1 card from your hand to the Graveyard to negate its activation and destroy the card.
The part I am interested in is shown. How exactly does it work?
OK, I understand that it works on card effects such as "Elemental Hero Flare Wingman" has and other direct damage like "Meteor of Destruction".
What I want to know is: does its effect work on cards that are taking your own life points as a payment, such as: "Fairy Box" and "Mirror Wall".

To put it in even more simple words:
Will my LP going to increace by 2000 per turn if I Have "Mirror wall" and "Prime Material Dragon" on my side of the field?

"inflict" not "pay"
its effect activates when an effect of a monster, trap or spell cause you direct damage
examples:
your opponents activates ookasi, prime material makes you gain 800 life points
flare wingman destroy one of your monster, prime material makes you gain the ammount of the attack of the destroyed monster
trap ehmm... dont wanna think

this card invest the damage you would recive, but only effect damage, a life points payment is not considered as damage(like fairy box)

It will not work on cost "damage", no. As this is not damage but just a cost you pay.

Paying Life Points and Maintenance Costs with Prime Material on the Field will not cause you to gain LP.