But that's not quite what you're looking for as I suspect it is quicker easier to unplug your USB and walk with it! There's tech's easily capable of all this, but the industry seems to work very hard to make it difficult to do what we want.
The problem he'll likely find is that moving the USB memory to another TV means it won't play. The new TV will see recordings made by another set, and so refuse to play them, or at least refuse to play any HD ones. This is all part of the digital economy. The major manufacturers.turers play by the rules. The powers that be are slowly closing all the loopholes and the 'free' options to pave the way for charging for stuff.
The rights holders for content don't want their shows ripped off - particularly HD recordings - because they want to keep selling them to TV companies/Streaming Service Suppliers and to the general public as downloads/rentals/disc-based media and box sets. It's understandable, albeit frustrating from a simple user's perspective when all that's really wanted is to play the content in a more convenient location.
Most people aren't pirates. The trouble is that this 'moving content' is the first step in pirating it too, and so by making it more difficult they then deter the casual/low-level piracy such as the guy who sells dodgy DVDs from a car boot.
The answer is to move the recorder. At first that doesn't seem feasible. However, there are small DVB-T/T2 receivers that are little bigger that a couple of Mars Bars side-by-side. They cost under £40 each and have the same record-to-USB feature as the TV. The connection to the TV is via HDMI. This won't be practical for everyone for lots of reasons. But for those who can go down this route it offers a simple and fairly low-tech solution to the problem.
Based on feedback from other FMs who have taken this advice, the results are close enough to the TV internal tuner recordings not to have to worry about quality. Also, the USB memory is playable on anynof the same model receiver. That's a bonus because it's easier to move some USB memory.