My new employer filed for H1B COS which got approved(effective immediately) but I’m still working with my current employer on F1. What to do since I’m no longer in F1 but I haven’t stopped working for my employer yet?
In this situation, you need to stop working for your current employer and start working for the H1B employer.
In your post you have mentioned that your COS is approved with immediate effect. Did you talk to the immigration lawyer of your H1B employer?
If it is first time cap-subject H1B approved with COS from F1 to H1B, the status change will happen effective 1st October. Talk to your lawyer to clarify.