I have the same situation when I extended my first H1B. I expressed my concern to the attorney of my company. I was told there is no problem for this. He also prepared a memorandum in case I have to apply visa oversea. Here I quoted some sentences that help you.
"Please note that by regulation, provided an H-1B transfer or extension petition is timely filed with the USCIS prior to the expiration date of beneficiary's current H-1B status, a beneficiary may lawfully continue to remain in the U.S. while the petition is pending.
In addition, please note that a beneficiary of an H-1B transfer petition is eligible for employment with the employer upon filing of the petition with the USCIS. It is not necessary to await an approval of the petition to begin work with the employer."
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"As previously discussed, an individual will be found to be lawfully present in the U.S. if a petition requesting an extension of nonimmigrant status is timely filed prior to the expiration of his or her current status."
"Please note that by regulation, provided an H-1B transfer or extension petition is timely filed with the USCIS prior to the expiration date of beneficiary's current H-1B status, a beneficiary may lawfully continue to remain in the U.S. while the petition is pending.
In addition, please note that a beneficiary of an H-1B transfer petition is eligible for employment with the employer upon filing of the petition with the USCIS. It is not necessary to await an approval of the petition to begin work with the employer."
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"As previously discussed, an individual will be found to be lawfully present in the U.S. if a petition requesting an extension of nonimmigrant status is timely filed prior to the expiration of his or her current status."
