H1b petition approved and got 1-797b can i change employer before stamping

Hi,

I just got h1b approved in feb 20. my opt is expiring on june 2020.
I have a contract job at Cisco. So my prime vendor wants to transfer my h1b as soon as possible.
because i am legally on opt right now.

My question is can I transfer it to other employer without h1b stamping.? Is it advisable to do so.?