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No, the filing of the extension of the EAD does not extend the work authorization while the I-765 is pending.
There is a different law that allows the principle visa holder of an L1 or H1B to be allowed to work for 240 days while their extension is pending.
240 Day Rule
Sec. 274a.12 says:
(20) A nonimmigrant alien within the class of aliens described in paragraphs (b)(2), (b)(5), (b)(8), (b)(9), (b)(10), (b)(11), (b)(12), (b)(13), (b)(14), (b)(16), and (b)(19) of this section whose status has expired but who has filed a timely application for an extension of such stay pursuant to §. 214.2 or 214.6 of this chapter. These aliens are authorized to continue employment with the same employer for a period not to exceed 240 days beginning on the date of the expiration of the authorized period of stay. Such authorization shall be subject to any conditions and limitations noted on the initial authorization. However, if the district director or service center director adjudicates the application prior to the expiration of this 240 day period and denies the application for extension of stay, the employment authorization under this paragraph shall automatically terminate upon notification of the denial decision. (Revised 1/1/94; 58 FR 69217)
That same rule does not apply to the dependent work authorization that is pending for a dependent.
Your wife has to wait for her new EAD card to work after this one expires.
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