I'm not talking about "identical" consciousnesses. I mean the same consciousness. The same consciousness cannot split into two, can it?
Either it is (and continues to be) the same consciousness, or it is not. If it were the same consciousness, then you would have a person who exists in two places at once.
Consciousness has no agreed upon definition to begin with, but I like to think of it as to what a whirlwind is to a bunch of air molecules (that is, an example of emergent behavior)
So your question is, are two whirlwinds with identical properties (same speed, same direction, shape etc) the same in one box of air, vs another identical box?
Well, "the same consciousness" it's not, as for example it occupies a different position in spacetime. It's an identical copy for a split second, and then they start diverging. Nothing so deep about any of this. When I copy a file from one disk to another, it's not the same file, they're identical copies for some time (usually, assuming no defects in the copying process), and will likely start diverging afterwards.