There are style converters. See post #4 at
https://www.keyboardforums.com/threads/transfering-registration-user-files.32647/#post-219983. As for the story in the video (which I only watched a little of), samples are copyrighted as musical recordings, but styles probably don't have the copyright issue. They are not recordings, nor are they compositions, I"m not sure what (if any) copyright could apply.
As for bringing in
sounds from other manufacturer's boards, Reuben basically has that covered, but there are tools made specifically to simplify the task of moving sounds between keyboards (or between keyboard and computer), albeit within limitations that Reuben also touched on. They're not going to sound
exactly the same as they did on the original (and the more faithful you want to get, the more the required memory can quickly grow to unmanageable proportions). But you can often get very usable approximations of sounds from other boards (or VSTs) using tools like SampleRobot, Samplit, Mainstage Auto Sampler, Extreme Sample Converter, or the tools from Chicken Systems (some are Mac, some are PC, some are cross-platform). It's a handy way to, for example, have the basic sounds you want from numerous sources in the one or two keyboards you may be performing with. (The board you're loading the sounds into does have to be one that has the ability to have new samples loaded into it, of course.) It does take some effort, but you by no means need to become a programmer. And there is no copyright issue if you own the source keyboard/VST and are sampling for your own use (hence the legality of all those tools).
Depending on the sound you're trying to "transfer," you may quickly get very acceptable results, or it could be quite a challenge. A piano sound, for example will be difficult, due to things like multiple velocity samples, long gradual decay, and any implementation of sympathetic resonances. Sounds that evolve over time are likewise difficult... in general, you'll want to turn off most effects and modulations and recreate those things on the other side. OTOH, many sounds can effectively come over quite easily. Ones that either quickly decay to nothingness or quickly decay to an unchanging looped sound are the easiest to work with, especially if they have few if any velocity variations.