I'll guess he's going to leave in place the 45 deg sweep fitting that's connected to the stack and replace everything downstream of that with pvc????? If that's correct then I would use a 3001 series Fernco Proflex coupling
. On the link click on models and you'll notice a section titled "Connecting Cast Iron, Plastic, or Steel to Copper" I would guess that the following coupling would fit your demensions though I suggest measuring the O.D yourself just to be sure:
3001-150 1-1/2" CI, PL. or ST. to 1-1/2" Copper or 1-1/4" PL. CK-115.
They're sold at most plumbing supply houses or even your local big box store.
Aside from the plumbing, is that newer plastic insulated romex wiring running through the studs or is it the round cloth covered wiring? If it's the cloth covered stuff I'd also consider replacing it and upgrading to a 20 amp circuit at the same time. And, think about running a circuit for a vent fan if you don't already have one.