Honestly any player can move between leagues and play well all the time, just everyone needs to adapt, I think it's obvious. But yes, there are some players who can't play in a new league right from the start, but in a new team in principle, I think it's much easier to adapt to a team than to a league
There are definitely also players out there that are having a pretty hard time to adapt whenever they are joining a new team or even a new team in a new league and there are several examples for that out there. Just take a look at Messi. He pretty much was the dominating player of football (together with Cristiano Ronaldo) in the last 10 years or so when he still was at Barca. Now at Paris Saint Germain he is still a great player but definitely not the same as he was back in Spain. Age may be one factor but that's only a part of the story. I think he is a player that just needs to fell comfortable to perform at his highes level.