H1B transfer and part-time H1B

[rameshchandra]

I'm working on H1B for comp-A for last few months, and comp-B filed my H1B visa transfer. After I talked to comp-A on my resignations, comp-A is telling they can file/ammend my current full time H1B visa to concurrent part time H1B for me.
Can I work for comp-A without letting comp-B know ? Is there any legal issues in this ? How long would this process take ?