"Chance on Hit" and Damage Conversion

I have got question regarding damage type conversion as well.

Take the top 20 Lightning Retaliation Archon as the example.

The Conduit of Divine Whispers converts 100% Aegis of Menhir physical and fire damage to piecing damage.
Mythical Scion of Burning Vengeance converts 100% Aegis of Menhir physical damage to lightning
Mythical Skybreach of Bulwark converts 100% Aegis of Menhir fire damage to lightning
Light Bringer’s Gargoyle girdle of Attack converts 60% piecing damage to fire.

In the demo video, the resultant damage of Aegis of Menhir is obviously lightning.

So what is the order of conversion? Which items will have higher priority to convert first?
Is it physical & fire → piecing → fire → lightning or
physical → lightning & fire → lightning before the Conduit conversion take effective?