Reward her when she is quiet, ignore her when she's not.
At the moment, your puppy is more persistent than you are, and each time you give in to her and go to her when she howls, you teach her that howling and barking and whining wins her what she wants - attention. You `break' before she does, so to speak. And you reinforce a behaviour that you desperately want to stop! And, unfortunately, each time you do it, it'll take longer the next time you try to ignore her.
This is going to be tough, but you HAVE to do this. She is smart, she will learn quickly.
Next time she does it, let her howl. I mean even if she howls for three hours. Stay out of her sight and DON'T GO NEAR HER. You know she's fine. You know she is not hungry, in pain or anything physical. She wants attention. DO NOT give it to her. But be there - even if it takes ages - for the EXACT moment she stops and is quiet. As soon as she is, you go to her, praise her, love her and give her a treat.
The next time you go away you will have to repeat the whole rigmarole again. But each time you ignore her, each time you stay away until she stops, each time you come back when she's quiet - and ONLY then - you will teach her what is acceptable. And she will learn.
Dogs do what's best for them. If howling gets her your attention, she'll howl. If staying quiet gets her your attention, she'll stay quiet.
She is a husky and when she's fully grown will have a howl like nothing you've ever heard. You must sort this out now while it is still a relatively minor problem. Sorting out four weeks of the wrong kind of attention is going to be A LOT easier than sorting it out after three years, when there will be all kinds of problems because she is bigger. Learning a new behaviour is very easy for dogs. Unlearning an old one is very, very difficult. And it will only get worse, trust me.
And you can't train her while you're not there. You'll need to do this while you are home. She needs to learn that you can be home, and not be spending ALL of your time with her. She needs to learn that almost more than she needs to learn not to howl when you're gone. Dogs will have separation anxiety until we teach them not to have it. And to do that, they need to be by themselves for periods of time while you are home. So that they know that being away from you is normal and natural and nothing to get upset about.
This method will work, no doubt - but you have to be strong, and more persistent than she is!!
