My perfect clone would recognize himself as ME, but would I be recognizing myself?
This sentence (by teel) sums it up perfectly.
But the same aporia is constitutive of the problem of identity and memory; it (re-)emerges as soon as you try to question, avoid or surpass mythological thinking of the "self" as "the little person inside," who was continuously there since you were born, night and day, who remained him/herself through all the changes, and who will be there till you die. Logically (mytho-logically) death is just another change for this "little person inside": he/she/it has to be there after you die; it can move elsewhere, up, down or into another body; pushing the "logic" one step further it even had to be there before "you" were born.
Now try to dispense with this mythological self-image altogether. What makes the continuity of "you" except memory which works only "backwards," which is not even "something" that "remains" but a narrative and imaginary reconstruction? Where is "actually" the little boy or girl you were?
Trying to escape mythology at this point only results in poorer mythology. This the WT version of re-creation illustrates. But the other versions, whether religious (soul, spirit) or secular (I, ego, self, subject) are only better inasmuch as you don't try to open the "box," i.e. to understand what your preferred word/notion for "you" actually stands for.