damage conversion question

The wiki says (paraphrased) that when damage is converted from type A to type B, the converted portion of the damage retains its original type (type A) for purposes of stat application (increases/reductions, more/less).

If I read that correctly this would mean that (example, not considering damage ranges):

start:
300 base phys damage
200 base lightning damage
50% converted phys to lightning

after conversion:
150 base phys damage
-> 150 lightning damage (phys -> lightning)
200 base lightning damage


In the wiki it says that converted damage can also become subject to conversions (following conversion order). Now, what I couldn't find any comment on is whether the type of a portion of converted damage is retained across multiple conversions. Meaning: If I added lightning to cold conversion to the previous example, would the portion of lightning damage (which was converted from phys) retain its physical type, when it is converted to cold damage?
Here is how I imagine this:

start:
300 base phys damage
200 base lightning damage
50% converted phys to lightning
50% converted lightning to cold

phys to lightning (step 1):
150 base phys damage
-> 150 lightning damage (phys -> lightning)
200 base lightning damage


lightning to cold (step 2):
150 base phys damage

100 base lightning damage
-> 100 cold damage (lightning -> cold)

75 lightning damage (phys -> lightning)
-> 75 cold damage (phys -> lightning -> cold)

I assume that each available portion of the damage(base lightning, and converted from phys) is individually converted using the specified conversion (50% to cold). If that is the case, then my question is whether the part of the lightning damage that was converted from phys, and is now further converted to cold damage (75 cold dmg) retains its original type, and can thereby be scaled by phys, lightning and cold stats.

thanks <:

ok, tested it in PoB. Everything I have hypothesized in my post is true (according to PoB). Damage gets converted like that, and retains all types of previous conversions.