From http://www.immigration-law.com/
10/03/2007: Hybrid Facts of I-485 Applicants Traveling in H or L Status and
Issue of Abandonment of I-485 Application
Currently the rule requires nonimmigrants other than H or L travel with an
Advance Parole and the nonimmigrants in H or L nonimmigrant status may
travel on H or L visa status without an advance parole. Careful analysis of
the rule indicates that the nonimmigrants must possess an "approved" Advance
Parole at the time of departure from the U.S.