You can change employers and recapture any time spent outside the U.S. since validity began on your H-1B. I do not see recapturing time as risky as we do so every day as long as you have sufficient evidence to prove your time outside the U.S. However, your employer's attorney has all of the details. I would recommend you consult formally with an attorney on the recapture issue.
If you, instead, choose to change status to H4 you can do so and then change status back to H-1B when you find a new employer. However, you cannot work in H4 status and, therefore, won't be able to work until your new H-1B is approved. Alternatively, if you change employers directly with your H-1B, you can begin working for the new employer upon receipt of the petition by USCIS. The change of employer petition can recapture your time.
You will need to watch your timeline extremely closely if you hope to file the Permanent Labor Certification with 365 days left on your H-1B time to allow for you to extend your H-1B time beyond 6 years. Please be mindful of that timeline and ensure that you strategically use the H4 if needed. You need Counsel to represent your interests.
I agree with my colleague's well reasoned opinion
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My colleague provides solid advice. However, I highly recommend that you speak with an immigration attorney about your specific eligiblity and plans. Since your employer has apparently indicated that he may not wish to file your extension, you may want to speak with an immigration attorney not associated with your employer.
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