I think he's in cuckoo land. When I was 17 I had a boyfriend of 22, it only lasted a few months and fizzled after about half a year, I ended it and discovered he had his heart set on us moving in together in a few months time. Which blows my mind looking back! As an adult I know how much cash it takes to keep a household running, how could a 22 year old have thought a 17 year old in college with a part time 8 hours per week job would have contributed at all? It's crazy.
What's his boyfriend's status, is he renting a room in a house share or his own place? I just don't see how he's able to afford his own place if he's an apprentice, it's hard enough on a full time NMW job.
Your son has no experience of work yet thinks he'll be able to cobble together, regularly, enough cash to live on to fund their life together.
I would say that you don't think it's a great idea but you'll support whatever decision he makes (emotionally, make it clear not financially) and ask him what he needs help with before he moves. Definitely sit with a budget sheet and sketch up what it'll cost them per month in rent, electricity, water, internet, phone bills, car (if partner has one) or public transport, council tax etc. And add on his estimates for food, socialising, cigarettes if they smoke, and then do the sums to show him how many hours per week he'll have to work to make all of that, given he won't even be eligible for adult NMW at his age. I would invite partner around too if he's amenable, as a 'I want to support you in this' and so you can see what his financial situation is too.
I am fairly sure once your fifteen year old realises he and his partner are gonna have to be working 60 hours per week, each, at jobs he may not want or enjoy, which will harm his continued education, he might not be so keen. And if he is? Great, he's not sleepwalking into it.
I'd be very wary of debt. Talk to him about money and debt. His partner's finances aren't really your concern but banks are throwing overdrafts and credit cards at young people as soon as they're eligible, the only way I was able to keep afloat at 18-22 with a severe health issue, despite working (but had lots of days off ad hoc due to hospital) was credit cards and loans, going bankrupt at 24 which has affected my life ever since. At his age without a solid grasp of money he likely is primed to fall into the trap of debt to keep things going.