H4 travel when H1 Visa tranfer is in process

[kr_mangesh]

Hi,

1. My Family is going for stamping on 1st June with my current I797B (valid till Oct19 through Employer A). So they will get visa stamped through Employer A

2. I will be joining Employer B on 19th June (based on Visa transfer Petition Receipt).

3. My Family is planning to come  US on 27th July

So my question is that can my family enter US on 27th July

-with H4 stamped (from my previous employer A on June 1st) and

- my latest I-797B receipt notice  (from my new employer B , Visa transfer will be in progress on 27th July)

Please suggest if there will be any issues. If yes , what should I do so that my family can enter in US in July.

Thanks