The only known way of making an exact copy of a quantum mechanical system involves destroying the original. Some people think that the way our mind works depends on quantum mechanical processes. If so, then you need quantum teleportation to preserve all the exact quantum states. But the process so far only works for individual atoms - so a long way from being able to teleport a human.
If it was possible, the duplicate presumably would think the same way but the original is destroyed.
If our memories are stored in a way that doesn't require quantum mechanical states, then you could use classical teleportation. Every atom the same in the same position (near enough). Would the result be an "identical twin" that has the same memories as you?
Even if quantum states are needed for your duplicate to work as a person, even if it also requires new physics such as gravitational collapse "quantum observation" - still, this imperfect copy with the same chemistry and arrangement of atoms but different quantum states, might have what it takes to start functioning as a person. After all surely heart, lungs, brain, everything would be working. So then it would make sense to ask if it also has the same memories as you.
Anyway the technology doesn't exist yet. Two things that seem almost impossible
Scanning the position of every atom in someone's body without progressively destroying them in the process - or indeed even with destroying but so rapidly you preserve all the information
Reconstructing a body from all that information with all the atoms in one place, so rapidly it doesn't fall apart or cease functioning as you try to build it (imagine trying to build a human body using a 3D printer over a period of many hours :) ).
And as for asking it as a thought experiment, I think so far nobody is quite sure how we are able to remember things. So it will be impossible for anyone to answer for sure.