I Recently Got A Puppy Who Was Paper Trained; How Do I Now Housebreak Him?

We got a puppy on Sunday; he’s an adorable and playful 15 week old cockapoo.
He was paper trained while at the store (dont worry he came from a reputable breeder and not a puppy mill) because he didn’t have all his shots yet.
He just got his first distemper shot (which is more common in my area (Brooklyn) than most others), so our Vet said it’s ok for him to go out for a short period of time so long as he doesn’t interact with other dogs, and we have to be very careful watching him.
So we’ve been using newspaper and puppy pads for the past three days. However, we do want to start housebreaking him.
I’m reading a book that says once a puppy is paper trained, he can’t be switched. I’m confused.
Can someone who has made the switch from paper to housebreaking help me make sure my puppy gets on the right track?