alt Hacker Newsam no expert in brain development, still have read about evolution. I like aspects of the way you mentioned this, but seems that putting cortex separately from fish brain isn't quite right. As you mentioned, the cortex is simply a part of the fish brain that evolved much (much, much) larger than a fish's. Maybe:
Fish Brain = brain stem + small cortex (+ other parts of brain)
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(evolved into)
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Sorry, know this is splitting hairs, but just thought it a useful distinction to make.
That's not quite right - a fish does not have a cortex.
The pallium of a fish and mammal are structured differently. A fish's (& bird's) pallium has a clustered (aka "nuclear") organization, while a mammal's has a mostly layered organization which is what is referred to as the cortex.
There is also more to a brain than just brainstem + pallium. In a vertebrate it's brainstem (aka hindbrain) + midbrain + forebrain, with the pallium being part of the forebrain.