With the recent glut of teleportation technologies showing up, we now have a situation where two [initially] identical copies of a person can exist at the same time.
Consequently, while their brains start out identical, they accumulate different experiences and memories.
Supposing we can't afford to keep these clones around long term, so the telecloning technology is used to make duplicates at remote locations, where the clone has the subjective experience of "being there", and when they're done with that they step into the "teleporter" that will take them home, where they are scanned and disintegrated.
The original is also taken into a corresponding machine which receives the scan, and then the clone's memories are spliced into the original. Essentially Total-Recall style.
So staying as close as possible to our current understanding of human neurology and the way in which memories are stored, how do we explain the operation of this technology, which manipulates a brain to combine all of the experience of two clones? Also, what caveats are there?
Leave the physics of actually manipulating the brain out of it. We have teleporters, so we use that technology to scan both brains and to beam out the original brain and beam it back in with the merged memories. It's the neurology that's interesting. Do you have to fundamentally rewire things in a form that is similar to neither of the originals, or do you just subtly tweak the strength of connections, or what? If the science is absent, invent it.
I assume that if the wrong person steps in there and their brains are found to be incompatible, the process aborts, and the clone does not die. This could, in some situations happen even when the clone is the right clone, but something serious has happened, like a head injury.
I acknowledge that the clone, being a perfect copy of the original and having all the same sense of self preservation may have reservations about stepping into a dematerialisation machine. To address this, we attempt to socially condition people before they're telecloned. Making them understand that when they wake up and discover that they are a clone, that the return trip which dematerialises them will not mean their death because the reintegration of their experiences will result in them appearing back home (among their friends and family, so they're motivated). This doesn't have to be accurate. They just have to believe it.