For spring semester, refer to the comment thumper1 made above about sequencing. This may or may not matter depending what major your child is doing (it wouldn’t have mattered for my older child but can definitely matter for some). For some majors it may make sense to wait till fall before transferring because of this. Your student should also try check to see if credit will actually transfer, but they may not know this upfront - I know at D19’s school, the final determination of what would transfer was only made after registration. I don’t know how common this is.
Finally, if he does decide to transfer, he should probably look at other options too. I’d guess there’s a decent chance he’d be accepted if the school had originally accepted him, but a plan B is always a good idea.