In the Cyberpunk genre (and others) people upload their minds to machines and, perhaps, gain a form of technological immortality. Because of the obvious analogy to the way computer memory works, it is appealing to take uploading the mind to be uploading memories. In fiction, the author simply decides whether it is the same person or not—but philosophers need to argue this matter.
While the idea of mind uploads might seem like a recent thing, philosophers have been considering this possibility seriously for a long time. On excellent example is John Locke. On his view, a person is their consciousness, and he considered the possibility that this consciousness could be transferred from one soul to another. Locke’s terminology can get a bit confusing since he distinguishes between person, body, soul, and consciousness. But suffice it to say that on his view, you are not your soul or body. But you are your consciousness. Crudely put, this consciousness can be considered to be your memory. As far back as your memory goes, you go. This is rather important: for you to achieve technological immortality (or as close as possible) it needs to be you that continues and not just someone like you.
Locke anticipates the science fiction idea of uploading your mind and considers the problems that arise if consciousness makes personal identity and it could be transferred or copied. His solution seems to be a cheat: he claims that God, in His goodness, would not allow this to happen. But if Locke is right about consciousness being the basis of personal identity and wrong about God not allowing it to be copied, then it would be at least metaphysically possible to upload your mind by copying your memories.
David Hume, an empiricist like Locke, presented an argument by intuition against Locke’s account: people believe that they can extend their identity beyond their memory. That is, I do not suppose that it was not me just because I forgot something. Rather, I suppose that it was me and that I merely forgot. Hume took the view that memory is used to discover personal identity—and then went off the rails and declared the matter of personal identity to be all about grammar rather than philosophy. But even if the memory approach to personal identity fails, there are other options. One simple approach is to cheat a lot and just talk about the mind (whatever it is) being uploaded. The mind would, of course, also need to be the person—otherwise it would not be you getting immortality.
Assuming the mind is the person, there are two possibilities: it can be copied/transferred or it cannot. If it cannot, then this sort of technological immortality is impossible.
Suppose that the mind can be copied. If it can be copied once, then there seems to be no reason why it cannot be copied multiple times. The problem is that what serves as the basis of personal identity is supposed to be what makes me who I am and makes me distinct from everyone else. If what is supposed to provide my distinct identity can be duplicated, then it cannot be the basis of my distinct identity. Locke, as noted above, “solves” this problem by divine intervention. However, without this there seems to be no reason why my mind could not be copied many times if it could be copied once. As such, a being might have a copy of my mind, just as it might have a copy of the files stored on the phone I own now. There seems to be a paradox here: to have technological immortality, then the mind must be copyable. But if it can be copied, then it is not the basis of personal identity—it is not what makes you the person you are, distinct from all other things. So, if your mind can be copied, you are not your mind and the copy will not be you. It will just be someone like you; a technological doppelganger. If your mind cannot be copied, then there is no technological immortality in the strict sense. So, for the copy to be you, it would need to possess whatever it is that made you the person you are and what distinguished you from all other things—that is, your personness and your distinctness. But perhaps this could be transferred.
One interesting possibility is that the mind could be transferred from a biological system to a new technological one. In this case, you would be transferred rather than copied—it would be like handing off a unique item as opposed to creating a copy. In this case you could achieve technological immortality. Your original body might keep living, but if you are transferred whatever that entity is it would no longer be you. It would be like a house you once occupied. This, of course, is analogous to possession: an entity takes over a new body by transferring into it.
As a final possibility, it is worth considering that the Buddha is right: there is no self. In this case, you can never upload yourself because there is no self to upload.