-
There are some issues with your plan but it doesn't matter much as it will all be removed before anyone else deals with it, at which point it will be pretty clear what's happening.
Having said that. You should not be pulling mains wires through the wall, it doesn't meet the regs (ok I've got that out of the way). Personally I would be running the TV power from the existing position by wiring the tv cord to the mains supply with the faceplate removed. I'm still not clear about the back box. Surface mounted or in the wall? If it's in the wall you would just use it to house the connectors.
Unless of course it's a special cable that provides power and signal to the tv, in which case of course you'll want to pull it through the wall and since no one will drill between the tv and cabinet it's unlikely to be a problem.
I'm planning to remove the socket altogether. It's currently about 1.5m from the floor and is designed to allow for a TV on a wall bracket to use the power cable there rather than down where sockets would usually be.
In reality, for this TV, it will just get in the way of a total flush mount. I want to:
Here's a super crude version of my plan with the existing TV in place...