Job change in US on Approved H1 but not stamped yet

I am currently on an L1 visa which is under a renewal process and I am staying on the 240 day grace period which is allowed while the L1 application is filed for renewal. I also have an approved H1 from the same employer but I do not have it stamped as I have not left US so far (My H1 was filed as counsular petition).

My question is whether I can change job on the approved H1 with only the approved petition or do I need to go to India to get the H1 activated first through the current employer. Also does this have any impact on the stamping incase this is a valid scenario and I can change jobs.

Thanks in advance for the help!!