there is a reason why people die, it's to get rid of the crappy old ideals and keep moving on (like how people didn't believe bacteria could exist (some countires they still believe that i think) when they clearly do and if no one realised bacteria existed we would still be dying to something that could be easily "cured"). it's called evolution.

that aside, i think the notion of immortality you put forth was downloading your memories to another body, and you keep doing that and you live on and on. (dangerous because not everyone likes to learn or see their flaws and do anything about it)
but then, is a body who has your memories still you?
i dont know... maybe having memories of someone else who is suppose to be you makes you that person since you have no memories of your own, but then, what's to say you'd still act the same?

if you 'download' your memories to a newborn baby who would become normally become someone who likes to murder for fun will that infant have all your memories and still want to murder even though you wouldn't? i say newborn baby because if you donwload your memories into something that has memories then you've taken someone's life if you wipe over them, and if you don't wipe over them then there's absolutely no chance that you've got the same person. the problem with a new born though is that i don't think they retain their memories. (does anyone remember being born?) therefore it's pointless downloading your memories to a new born.

so maybe you don't go down the new born route, maybe you take a teenager and it's ethically correct to kill them in favour of some old geezer who just didn't want to die and who doesn't add any value to the world by being stuck in their ways.
that implies that you can just download yourself to another person.
and following the notions of Ghost in the Shell what happens if you can download other people's memories? their experience becomes yours? you know what they know. you could trick yourself into being another person. at what point do you stop being yourself and become someone else? people will eventually all become the same because no new source of identity will ever arise because everyone wants to be awesome.
if you can do stuff like that then surely hacking into other people isn't that far off either. make them do things they normally wouldn't, make them have memories they never had

you ask, would the copy have a 'soul', i have no official religion myself but i don't think the soul is capturable or digitizable. the 'soul' would transfer to the other body provided the other body doesn't have one and that the 'soul' is willing and capable. although, i dunno if that's possible.. you can leave your body anytime if you know how, but i dont know if you can disconnect yourself from it and connect permanently to another

so... is it feasible to download your memories into someone else to achieve a sense of immortality? maybe we have the technology.. i dont know..
is it moral? the simple answer... hell no. why stop evolution? that and even if you could do it, you'd have to "kill" someone to transfer your memories.
then there's the whole what-gives-you-the-right-to-take-someones-life-thing and the whole what-gives-you-the-right-to-live-on-past-your-expiration-date?