Don't forget the ex-spouse too. If the ex-wife feels one of her children is being shrifted, you better believe she will make a problem for your husband. She will really create a problem for you both. She may even demand a change of custody due to her ex-husband's unwillingness to even provide a bedroom for her child. You may or may not think she would do such a thing, but believe me ex-spouses can do unimaginable things throughout and after a divorce...especially if they think they, or their children, are being short-changed somehow. This may get nasty for you. Just be careful and really think this through.
Also, this will set up a less than desirable situation for the stepchildren. If there is no place for the stepson to call his own in his father's house, his visits will become less frequent over time and perhaps eventually stop all together. Why would anyone want to go to someone's house where there is no place for them. Especially a teenager. He'll feel cramped and overcome with baby this and baby that. Where can he escape it at your house...no where if he doesn't have a room.
If I may suggest, if you have a basement you could fix up for him, he, along with most other teen age boys would love it. If it's cold and damp, that can be addressed. It doesn't have to be perfect. Temporary walls with paneling, or fabric will work. A nice roll of carpet remnant for the floor, a dehumidifyer and space heater for extra heat will work. A nice electric blanket for the bed will help too.
Also, a word of advice, no matter who does what, you, as the step parent will almost always be blamed. The step kids won't ever think ill of their father, they will most likely blame you, the outsider, for whatever goes wrong in their relationship with their father. True or untrue that's usually the way it shakes out for the kids.