H1-B expiring . Can I still transfer after H1 expiry date.

I have been on H1 for 12 years since I-140 has been filed.
My current H1 expires June 15, 2019 and the present employer has filed a H1 extension on June 5th 2019.

While waiting, can I transfer my H1 to another employer past the June 15th date - when my current H1 and I-94 expires ?