Dogs have separation anxiety for a reason. Because, they are insecure. They JUST moved. He doesn't know what's what right now. He is insecure, anxious, and unsure of his surrounds. This will be magnified many, many times...if it's an older dog. So...slap a shock color on it, and make the dog more afraid and insecure. Awesome. I won't even get into my feelings on shock collars. It's HER responsibility to take care of the dog, not an unethical collar. She needs to start making the dog feel secure. If she can get out of the house so long, then she is well enough to take the dog out every day. He needs to smell and explore his surroundings. She should do this every day, regardless. If she can't, someone needs to, or she shouldn't have a dog. Leave a Kong toy down for him, with peanut butter, as she leaves. Really, he needs to know his surroundings. He is sniffing and hearing a billion things he can't see right now. That is pretty terrifying for a dog. Wesities NEED companionship. She should know this about the breed she brought home. Without it, they don't thrive. They bark. A LOT. They also need exercise every day. They may be smaller, but they are terriers. HIGH energy, and need to get out. Again, SHE should know this about her breed. Please, don't use a shock collar. If she can't take care of her dog, she shouldn't have it. Her dogs has NEEDS, and the breed has NEEDS. If the dog is sitting inside all day and not getting it's heart rate up (at least an hour a day) she needs another breed. This breed will not work for her.
P.S.
Shock collars should NEVER be used unsupervised. They should ONLy be used when an owner is home.