If you object to the term "mind", just leave it out and read "brain and mind" as just "brain". I'm a physicalist so I don't think the mind is something separate from the brain anyway, so it's all the same to me.
If a jellyfish was able to have a conversation with you where it credibly described what it's like to be conscious, would you reject it because it doesn't have a brain and therefore cannot have a mind in the same sense as you?
I don’t object to “mind”, but it’s famously unprovable whether other beings we presume to be conscious actually experience internal mental states. See also: qualia, p-zombies, the hard problem of consciousness.
> it’s famously unprovable whether other beings we presume to be conscious actually experience internal mental states
It's also famously unprovable that there is not an invisible dragon in my garage that cannot be detected by any means whatever, to use Carl Sagan's example. That doesn't mean such an idea is worth discussing or including in your thought processes.