The idea of somehow uploading the state of the brain into an artificial one is often mentioned not just as science fiction, but also as some sort of transhumanist hope that is being worked on. This may be an interesting exercise to entertain, a research goal to pursue, but it's definitely doomed to fail, because it's a flawed idea on multiple levels.
The brain is a physical and very dynamic object, one built by cells which are living things. Neurons are destroyed continuously and are partly generated. Nutrition, physical trauma and many more subtle things, all affect the continuous changes of the brain. Neurons in time can establish different connections... everything is so dynamic and biological, it's a system so complex and so dependent on external environment that it's practically impossible to somehow recreate the necessary complete system that would operate, respond and evolve even remotely like the actual thing.
So, a digital brain that by some incredibly futuristic technology would be able to initially mirror an original biological brain, would progressively diverge from the original brain, because of fundamental mechanics but also because it couldn't possibly be exposed to the same effects, unless the digital brain would be so advanced that would for example be able to sample the blood of the host for drugs and alcohol and simulate those effect that a normal brain would have... but here we'd be talking about an understanding and a simulation so complex that by the time that one would be able to achieve that, the human brain would be practically irrelevant.
Of course one could simply decide to switch to a digital brain and go along with its relatively crude simulation, perhaps unable to process external effects related to what one ingests and breathes in. That would definitely quickly become something very different, where, paradoxically, the potential plasticity of that artificial brain may have to be limited to mimic the real thing using some arbitrary and approximative parameters. That is assuming that one may even reach that level of sophistication that today is unthinkable.
In conclusion, the digital brain replacing a biological one is just a flawed idea. If the goal is some sort of immortality, then one either tackles it from a biological point of view. The alternative would be to recreate a perfect biological simulation, basically a small virtual universe that mirrors the laws of nature, while also operating under the laws of nature (hard/impossible task in itself). Otherwise one simply decides to switch into some technology that is incredibly advanced, but simplified, and that is tweaked to mimic the real thing with some sort of containment programming put in to avoid that the artificial brain takes its own wild evolutionary path... which doesn't sound fun at all.