Regarding h1b cancellation and h4 stamping

Hi. I got my h1b visa approved last year but had to come to India before I started to work. I recently learned my employer has still not cancelled my work visa? I was previously on a h4 visa and my employer says it’s automatically cancelled. I intend to go back to the States now. My question is if my employer cancels my h1b visa can I enter the U.S. with my previous h4 visa or do I need to go for a new stamping for h4 visa? Please advice on my status.

You cane enter on H4 if your stamp still has validity…

Also your H1 was approved earlier, so you must be able to go for cap-exemption now, as you already had an approved petition. But the best option is to enter US on H4 (if there is validity and then go for transfer/cap-exempt)