The new one will have the same memory and physical body, but it isn't the original person, from their point of view the life ended.
The problem with that idea is that it speaking from a point of view
that does not exist. There are basically two views one can have about teleporters, and although I think both are compatible with materialism as they are functionally identical, I think one is more problematic than the other.
The first view is what I call the
vertical view.
In this view Person A lives, until s/he enters the teleporter, information is transferred to the receiver where Person A' is created. Speaking from the viewpoint at 1, Person A is dead. Problem is, this viewpoint does not really exist. There is no Person A to have this viewpoint. To see how strange it can be to discuss a viewpoint that doesn't exist, consider that we then can also discuss the non-existing viewpoint of Person A' at point 2. If we worry about Person A dying in the experiment, should we not also consider that Person A' will never exist if we do not perform the experiment?
If we think Person A will die, that is to say his/her identity will disappear into nothingness, isn't it also true that the identity of Person A' comes from nothingness? Of course we know this isn't true. His/her identity comes from Person A, which means the identity of Person A hasn't disappeared into nothingness but has been used to create Person A'.
To avoid discussing non-existing points of view, we can take the
horizontal view:
In this view, when Person A enters the teleporter, s/he doesn't die, but is transformed into a signal that is transferred to the receiver, where the signal is transformed to Person A'. Is Person A' completely identical to Person A? No, Person A' has experienced something that Person A had not, and experiences change people. In this horizontal view if Person A does not disappear during the transfer, so that both sender and receiver work as a copier, Person A also doesn't step out of the sender identical to how s/he entered it. Being scanned and copied is also an experience that changes a person. Whether one uses a teleporter or a telecopier, the person who had not stepped into the device ceases to exist, and a person who has stepped into it is created, and that is not different from any other device.