Work for current employer under F1 though H1B approved with different employer

[Student4]

I am currrently working for an employer under F1 OPT valid until May 2018 but I got an offer from a different employer which is a non-profit organization and they have applied for my H1B cap exmpt visa under premium processing. I heard from my attorney that they received an email from USCIS that my H1B has been approved and the official mail will be sent to them soon. Now my query is: though my H1B has been approved for a diffrent employer can I still work for my current employer for few more weeks or do I need to stop working for my current employer immidiately?

Can someone please help me? Thanks in advance.