Unless the employer is not subject to the H cap, there are no more visas available until October 2014. As a basic matter, a person is allowed to have an H while a GC application is pending. She would want to discuss this option with her sponsoring employer in January 2014 and then file on April 1.
Theoretically, yes, she could. However, practically speaking, since the H-1B quota has been reached for this year, there are no more H-1B visas unless she will be working for an employer that is cap-exempt.
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