The problem with AP for H-1 holders is that you don't gain anything by applying for it.
Please take a look at the following thread. Also note that the instructions for the I-131 state that H-1 + I-485 applicants do not need AP.
Or look at the following article then decided if AP is for you. Article: The H-1B Visa and Advance Parole
Please take a look at the following thread. Also note that the instructions for the I-131 state that H-1 + I-485 applicants do not need AP.
Or look at the following article then decided if AP is for you. Article: The H-1B Visa and Advance Parole