If it is a true 'Star Trek' type transporter, I don't see the problem. If the transported 'me' is identical in every particular to the destroyed pre-transported me (same height, weight, hair colour, memories, emotional balance, predilection for bathing in syrup and so on), I fail to see any dilemma.
A difference which makes no difference is no difference.
Boru
A difference which makes no difference is no difference.
Boru
‘I can’t be having with this.’ - Esmeralda Weatherwax