Advice on how to respond to employment eligibility questions on applications (even with an active H1B)

I am currently on H1B in the US, and i am applying to other companies by the side.
However, knowing fully well that when i join a new company, the new company will need to apply for transfer of my H1B etc. i see these 2 questions often in applications and wondering if my response should be a “Yes” or a “No”

(a) Are you legally authorized to work for any company in the country for which you are applying for employment?

(b) Will you now or in the future require us to commence (“sponsor”) an immigration case in order to employ you (for example, H-1B or other employment-based immigration case)?

How do i respond to these questions? In the past, i have responded “Yes” to both questions and my application didn’t progress to the next stage.

Any idea on how to navigate this please, so i don’t shoot myself on the foot.

Many thanks for your help

A should be no, B should be yes. H1B is only authorized to work for the sponsoring employer.

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