Quoting from your other post as background, to make sure that everybody is on the same page: "My girlfriend works for a small business which sells items. She started there two months ago and did not sign any papers. When she applied, she was told that she would be getting a 12-hour work week. However, her manager (the owner of the business) seems to randomly drop her hours in times in which there seems to be no demand (e.g., when there is bad weather, and no one probably will come by to buy anything). This has gotten to the point where the amount of hours my girlfriend worked in the last three weeks were 8, 6, and 3 hours respectively"
Given that her manager has been jerking her around ever since she started working for him, she doesn't owe him anything and that includes her notice. He hasn't done anything to deserve her respect and in my book, he should get none. If I were her, I'd start on the new job and I'd let him figure out that I am not available the next time he calls - I am not picking up the phone and he can talk to my answering machine for all I care. Those who treat me fairly get the two-week notice. Those who don't get what I feel like giving them - usually, nothing.
Once upon a time, I gave my two-week notice to a boss whom I knew to be unethical. While his underling promised to give me my accrued vacation - small reward for the 60-hour weeks I put in - his boss proceeded to cheat me of both the accrued vacation and my last two-week's pay. Not particularly funny considering that I had two dependents. My attitude is that her manager did not keep his word regarding her hours. He caused her financial hardship, disrupted her schedule and caused an awkward moment for her whenever she had to mention her reason for leaving at an interview, so screw him.