He should definitely try to stick at what he's doing. Teaching wise they are more than halfway through, even though that feels weird to say in January.
I teach on these sort of courses and although colleges have their own rules they can usually progress onto a level 2 course if they get at least merits on their level 1 course and have attendance above 90%. Some courses have higher GCSE requirements than others but your son has passed functional skills level 2 so that should be okay, and academically he should be able to get merits or distinctions at level 1 if he puts the work in.
School students bring in their school reports to interviews so the college has a good idea of what their GCSE grades will be. They might have already filled up the business course for next year but your son could ask if there's a waiting list.
As for the technical skills unit in his current course, if it's btec you can find the specification online. Maybe there will be aspects he is more interested in coming up. Maybe it is really easy, level 1 is easy. The hard part will be in hitting the distinction criteria rather than scraping a pass, and that means listening to the teachers rather than arguing or back chatting. You can't argue with the mark scheme. If you don't do what's asked you don't get the marks. Teenagers do sometimes struggle with this, at an age where their brains tell them they know better than the boomers who are teaching them.
If they argue or backchat, or skip lessons etc. this will likely be visible to the person interviewing them for the next course, so if this is where your son might have issues he'd have better luck applying to another college instead. If his grades aren't merit or distinction he could ask if he's missed the deadlines to improve those assignments. If his attendance is below 90% he might be able to bring his average up if he is 100% from now onwards.
Good luck with it.