Remember, the adult will growl to let puppy know she's pushing her luck. You need to just watch and step back a few minutes to see how it goes. As long as the adult isn't hurting the puppy (and growling, snarling or snapping AT her isn't hurting her), just let things work themselves out. If puppy Insists on continuing after getting a warning or two, then remove her.
Puppy needs to learn dog communication skills and learn some manners, and the best one to teach her is an adult. Reading dog language is important for her to learn so that when she meets strange dogs she'll know what the signals for different emotions are.
I would get the adult to a Vet to have her checked over, immediately, if you haven't already. If she's feeling bad or is in pain, she'll be more grumpy. Plus, you need to know that she's healthy enough to be with the puppy and won't infect her with something. Until you do this, she really shouldn't be with the puppy. Once she has a clean bill of health, let them get used to one another in increments, and give them together time and apart time. Interact with them individually, and then together, as part of the family.