Declawing requires the amputation of the tip of all the "fingers" of the claws. Imagine having the nail portion of all your fingers removed down to the first joint. The dog may never use her front feet again due to the severe pain. It would be considered mutilation.
Cats have retractable claws, and dogs do not, so the procedure for declawing does not affect cats quite as much, though they too go through a lot of pain until healed.
Jack Russells are extremely active dogs, and I believe money would best be spent on professional training, with an animal behaviorist or a veterinary behaviorist. Jack's also need lots of activity to burn off the energy. If you or your friend can find a person who can jog with the dog, or take him to a dog park to expel some of the excess energy, it could help. Training a dog not to jump is usually fairly easy, especially if food motivated, but it takes time and consistancy. Until trained please see if your friend can wear thick sleeves and long thick pants, and keep the claws very short and have them dremmeled to smoothness by a groomer or veterinarian
I am so sorry to bust in here, because the vet will have some good answers for you I am sure. But I do feel quite strongly about this.
I know it's too late now. Your friend has the puppy and has become fond of it. But this is exactly the wrong kind of dog for her to have. This is a highly-active intelligent breed, with high exercise demands which it cannot help.
My feeling about removing its claws as a solution to this problem is that it won't work. The active energetic little thing will start to use its teeth instead! or start doing other things to burn off its energy.
This lady is just not capable of giving the puppy what it really needs all on her own. It needs quite a lot of daily activity. And it does need proper, consistent, puppy training. I do believe there is no such thing as an untrainable dog, and to give up on its 'education' at this stage in its life is to condemn it to being a 'bad dog' for the rest of its life!
Jack Russells, and JR mixes are very hard to train, (not as easy as say, retrievers, or Viszlas.) But even they, with the proper training, do respond.
Apart from employing a behaviorist and puppy trainer, your friend also needs to employ a professional dog-walker. That dog needs to be outdoors, running, burning off stored-up youthful energy!
Then after some work, she will have a good companion, and a well behaved dog.
Also, has anyone thought about what is going to happen to the puppy if something were to happen to her? I do hope there is a good plan in place for its future. It could live for 15 years.