I wouldn't let him move in at all,
When I was 19 my parents let my boyfriend at the time move in with us, it was actually their suggestion, he wasn't very welcome at his mums house due to constant arguing, and he practically spent all of his time at our house anyway.
I thought it was a good idea and then very quickly I ended up hating it. I felt like I had no space of my own, of course, still living with my parents, there was only really my bedroom that was 'mine' - so having somebody come into that space with their stuff, and using that as their space too, wound me up - I just felt like he was intruding and I didn't have anything of my own. We ended up arguing none stop, or he would argue with my dad none stop. He was a very difficult person to live with, and it added so much tension to the relationship between me and my parents too. He worked odd shifts, and I worked 8-6, so on days he was off work, I always had him, my dad or my mum calling me to tell me about an argument and it was just massively stressful. He was very disrespectful towards my parents and me, never did anything to contribute to the house, so I quickly realised why he argued with his mum so much 😳
I ended up asking him to leave/find somewhere else to live, I just couldn't handle it. He walked out there and then & said a lot of nasty things to me on his way out - but he refused to get any of his belongings for well over a week. When he did return to get his things, he spoke to me like crap, told me how he'd been sleeping around for the 3 years we were together - got in my face shouting and launched a lot of my belongings across the room at me, he acted very violently and my dad ended up almost fighting with him.
I'd want to know exactly why your DS's BF has been arguing with his mum, but I would also refuse to allow him to move in. Your DS is 17, and this could turn out horribly for him, especially with the BF's previous behaviours.
I really hope you're ok OP, it can't be easy going through this when you only want what's best for your DS. I hope your DS can also understand too xx