COS- H4 (i539) and i797 H1 approved same time

[ramkrs80]

I lost my job and applied for COS to H4 and it got approved on Nov 26th.

 

My prospective company's H1B got approved (i797) got approved on Nov 28th (until 2017) with my existing i94 (which is valid until September 2016) . 

 

Since my H1 got approved almost during the same time, can I start working on H1B immediately ?

 

Please advise on what steps need to be taken next.