H4 travel on valid I-797which was from old employer

Hi there,

Please clarify on below scenario questions,

Myself and my wife have valid I-797’s approval for H1 and H4 respectively until Dec-2020 with employer A. I have recently switched to employer B and they processed my H1 transfer in regular and waiting for approval. No changes to H4 with employer B, my wife is still in US with H4 I-797 which was from employer A.
Note: Our visa’s are not stamped.

Questions:

  1. Do I need to ask employer B for her new H4 ?
  2. If my wife travels India now, Does she is eligible to get stamped with employer A H4- I-797 by providing my H1 I-797 from employer A and receipt notice of H1 from employer B?

Appreciate assistance.