If it says H4 it should have 3 prongs and your stock connector should plug right in. The back of the factory connector is like a lid and there are 3 small tabs the it snaps into, once you get the back lid open you can remove the metal connectors by pushing the plastic tabs that are in the center of them.
If the light has a trim ring use a rubber jar lid remover to spin it free, use a lot of pressure as it is a pain, then there will be an inner retention ring that will spin off.
Here is how to snake the factory wires once the connector is apart.
Some lights holes my be to small to snake the L shaped connectors, remove the swivel base then remove the main part of the mount from the housing. Ream an oval shaped hole in the mount base then a matching one in the light housing. Snake the wires through the mount first then through the housing after every thing is run bolt the base back onto the housing then reattach the swivel base.
Just noticed your pic when I went to post this. It looks like your light is has 3 wires but is grounded inside the housing so I would guess going yellow to yellow and green to red, then ground the black wire to the mount.