Say I had a cellphone, let's call it cellphone A, and made a perfect copy of it - SIM card and all - and let's call this one cellphone B.
Normally, your SIM card would be impossible to clone (it contains a secret that can't be read, but is used by the processor in the SIM card to en- and decrypt specific things, which doesn't allow you to "get" that secret). But, of course, the entity that produces the SIM card might choose to produce two identical ones. Or, you know, time travel.
Anyway, the network would detect that two phones with identical subscriber identities try to log on the network. Something similar can happen when your phone wanders from one cell tower to the next, when something on the network has gone missing, so that the first tower didn't notice you were gone.
So, I'd expect the network to "ask" the phone that was already logged into the network to verify it's still there. It will be. The new one will still try to log on.
The network will throw out one, or the other, or both or at the very least not allow both to make calls / use data at the same time.
How to handle that situation is completely up to the network, but you can be certain that nothing like "both phones ring at once", "both get the same text messages" or "when one makes a call, the other can listen in" happens: that's simply not how these networks work; there's central databases that match SIM cards to subscribers.