Hypothetical for DMs: You're running a game (around 7th level PCs) and one of your players moves away.
Online gaming with this person is not an option? Setting up a video conference, FaceTime, Zoom, etc simply not possible? I work around whatever needed to be worked around to keep that player in the game. Only if that's not an option would I move on from there.
You continue on a player down, but meet someone new, speak with them and decide they'd be a good fit with your group. You tell the player about your game and they say they're interested and - excitedly - ask if they can bring in a beloved PC they had been playing in a game that fizzled out.
I'd be incredibly leery of this. In my experience a lot of people are clamoring to play 5E and their characters but not really caring about the specific game or setting. The desire to play any game is greater than the desire to play any specific game, if that makes sense. Characters specifically made for the game you're actually playing are an infinitely better fit than something pulled in from elsewhere.
They pull out the character sheet and you can see that it is a balanced PC and - mechanically speaking - there are no issues with a PC like it joining the game.
The mechanics are maybe 10% of the question. The other 90% is the lore, the setting, the other characters, the group dynamic amongst the players, etc. I'm way more concerned about the rest than the mechanics.
How would you approach the situation?
If there's absolutely no way to keep the original player, then I'd consider a new player.
If there's absolutely no way to get the player to make a character suited to this game, then I'd consider a transferred character.
Characters are not precious. They shouldn't be treated as such. It's a simple matter to make a new character. In my experience, it's a similar situation to the player who's 1st-level character with 0 XP has a 40-page backstory. The player already has a fixed and unalterable idea of who their character is, what they'll do, and how they'll act/react in situations. This will lead to more problems than necessary.