New employer start date after current H1 expiration

[ramcrypto7]

Hello,

My current employer A, has my H1 petition valid until 06/27/19 and I-94 until 07/07/19.

I received an offer from company B and they filed for my H1 on 10/31/2018 and after an RFE it got approved via premium processing on 06/11/19 with validity start date of 10/31/2018 to 09/24/2021.

Company B wants me to start on 07/01/2019. 

If company A doesn't file for an extension, would there be any issue if I join company B on 07/01/19  ?

As there are 3 days between my current H1 expiration with company A and the start date at company B, I'm concerned if it would cause any issue down the road.

Please advise!